Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
The Catacombs
The Catacombs are accessible through the graveyard area of Firelink Shrine, which itself can be easy to miss even if you're looking for it. From the bonfire, look for the gloomy fellow sitting along the wall. To the right of him a bit, some steps lead to an opening in the wall. You can head through that opening, then diagonally left and through another opening. Walk straight through another door frame and you'll be in an area with a huge pit. A strange creature likely occupies the pit by the time you're ready for an actual run at the Catacombs.
Head forward along the left side of the pit and climb some stairs that lead left from there. Now start to the right. You can climb up some steps to find yourself on a high ledge overlooking the area with the pit. You can walk around up there and find a Soul of a Lost Undead on a corpse, or you can find a massive bird.
Otherwise, ignore the steps and head forward past their base to arrive on a ledge overlooking the graveyard. It's full of graves, just like you'd expect, and therefore difficult to miss.
As you start through the graveyard, you'll find your adventures interrupted by skeletons. They assemble from the bones lying on the ground and will rush to attack you a few at a time. You can easily take them out with melee attacks and keep moving to find a Large Soul of a Lost Undead. Continue along the main trail through the graveyard and as you approach a larger tomb, a huge skeleton will emerge from the ground. Back away and toss fire his way to scorch him. Then check the tombstone that he was guarding to find the Zweihander, a powerful sword. You can head out on a nearby ledge to also find the Binoculars.
Up the hill and to the right from where you found the sword, there's another pile of huge bones waiting among some graves, near a corpse. Defeat that skeleton, then check the corpse to find the Winged Spear.
Also not far from where you found the Zweihander weapon (and not far from where you can check a corpse for the Caduceus Round Shield), you can head downhill and search along the edge of the cliff. Some steps descend from there, pressed tightly against the cliff wall. If you follow them, they'll lead down for quite some time before entering a cave. As you continue into the cave (which is dark enough that you'll want to bring a light source), text will flash on-screen to let you know that you've just entered the Catacombs.
As you start forward through the catacombs, the first thing you'll face is a skeleton. You should be able to defeat him easily enough, but if you're not using a divine weapon he'll just come back to life because a nearby necromancer keeps reviving surrounding enemies once they are killed with anything else. You need to take out that fellow as soon as possible, but he'll be out of range for quite awhile.
To find him, you should mostly ignore the skeletons to the extent that is possible as you descend through the cave. You can't see much as you first visit, so you'll want to feel your way forward. Head down the long staircase that descends into the area, keeping to the right against the wall until you reach the base of those stairs. You'll have to battle or avoid two or three of the skeletons on the way. When you reach the base of the stairs, you'll find yourself in a larger and more open area. Now start to the left through a doorway.

You'll definitely pick up more skeletons as you're starting toward the left, if you don't stop to kill them. Keep moving if you're just trying to elude them, though, and try to stay ahead of them. You'll pass through another room that is an apparent dead end, which contains more skeletons. You can head along the side of that room and find an opening. Drop through it and continue down a corridor to descend to a chamber where there's a waiting bonfire. There's also a necromancer, though, and you'll need to defeat him (and any skeletons who may be closely tailing you) before you can put the bonfire to use. When you defeat the necromancer, he may drop the Red and White Round Shield. Some good news is that he also won't be returning, even when you rest at the bonfire. Some bad news is that there are more necromancers throughout the area.

Clearly, it's in your best interests to continue finding and defeating the necromancers so that your efforts against any skeletons in the area are a bit more helpful. It's time to start searching for the next necromancer.
Near the bonfire, there's a strange device on the wall. You can push a lever on it. Doing so will cause something to happen in the preceding room. Head back up the stairs you descended to reach the bonfire and look to the left. You should now see an opening with bluish light issuing forth. Head through that opening and be prepared for a skeleton to attack you near the top of the stairs. He's not worth bothering with because a necromancer is on a ledge across a gap and it will repeatedly revive the skeleton even if you defeat it.

Head down along a trail that descends toward the left and as you go you'll have to battle or avoid a few more skeletons at the base of a trail. A stone bridge allows you to ascend back to the right from there, in the direction of the industrious necromancer. Head up across it and through a door to the right, where you'll notice an opening on the wall to your upper left. Skeletons are up here, including an archer that will try to pick you off as you explore the adjoining area. He's difficult to reach from low ground, so just keep him in mind as you press forward.
Continuing forward, you'll reach the necromancer who was pelting you with fire a moment ago. He's scared of you when he gets close and will try to run through an area thickly populated by skeletons. You need to chase him down and kill him before he gets far, then tend to any skeletons around him that the chase has roused.
Proceeding in the direction the necromancer ran, you'll find an opening to the right. You can obtain the Lucerne sword from a corpse lying on a shelf there, but there are two skeletons to defeat also. Further along the same main corridor, you can head left to reach the room where the skeletons tried to snipe you from above. Defeat them, then check around for the Large Soul of a Nameless Soldier on a corpse.
There are two options that seem to allow you precede now, both ahead of you. Any paths to the left merely let you drop down to the area you've already explored, though. Start through the opening to the right and watch ahead of you. There's a stone bridge leading to a waiting necromancer, but you can't cross it because spikes protrude from its surface.

The trick is to run along the trail that leads to the right. This trail is densely populated by regenerating skeletons, and there's another hazard you might not anticipate: statues along the right side of the trap may attack. They don't do anything especially aggressive, just stand there, but dangerous spikes protrude swiftly like the quills of a porcupine and you can take some damage if you're too near. Rush past them and the skeletons to find a Soul of a Proud Knight at the end of the trail. You may also notice a bonfire through the wall to the right, but you can't reach it at this time. Your main reason for coming along the trail is a second lever that you can push. Do so and the spikes on the stone archway will lower.
Now return to the stone archway and head swiftly across it, hopefully without too many skeletons chasing you. There's a necromancer on the far side who will try to pelt you with magic, plus there are a number of skeletons that will rush anxiously forward to meet you. Clear them out while avoiding the magic shots from the necromancer, then take out the necromancer himself.

Past where you found the necromancer, the path splits. There's an opening to your right and there's a room up some steps to the left. Only go through the opening if you want to backtrack for no apparent benefit. Along that route, you can head toward the center of the room and step into the left of the two open caskets. You'll fall through the floor into a lower passage, which is lined by the spike-producing traps. Head along that passage with your shield raised to find a ladder at the end. From the top of that ladder, head left to find and fall through another open casket. You'll land in the area near where you pushed the second lever (to lower the spikes on the archway). No apparent benefit.

Going left at the split in the path leads somewhere more interesting. You'll find yourself at the top of a tall vertical shaft. As you descend along stairs on the edge of that circular shaft, you'll face numerous skeletons. Defeating them will only give you a brief respite, as they regenerate fairly quickly. You should focus on descending. You can find two Soul of a Proud Warrior items in the rooms to the right, and partway down you'll also find a statue with a switch that you can and should push.
After pushing the switch, you can take an optional detour. Continue down along the steps and when you reach the very edge, roll forward or take a fast-moving step off the ledge (if you're going too slowly, you'll fall to your death) and drop straight down to a lower ledge. You will likely take some damage from the fall, even when it is done properly. Continue making small drops to subsequent ledges and finally you'll arrive at the bottom, where there is a hole in the floor. Drop through it and ahead of you, a huge fellow with a scythe will appear. He knocks a hole in the wall to the right and invites you to head through it so that you don't spoil his focus. You can talk to him when he returns to the back wall and you'll find out that he's a blacksmith who can create fire-based gear for you. When you're ready to leave, head through the opening the blacksmith created and climb some stairs. At the top, you'll find yourself in an area with rolling pinwheel skeletons. You've found the shortest route to that area, but there are good reasons to get there by a longer route. Keep the detour in mind for when you're ready to head quickly to the boss from the nearest bonfire, but for now return to your exploration.
Once you're done with the shortcut detour, head back up the stairs from where you tripped the most recent switch. When you reach the larger area partway up the shaft, look left and there's a new route you can follow. However, it's worth making a detour first. To the right of that new path, there's a weak wall. Break through it and investigate the area beyond. As you battle skeletons, you'll work to the end of a path where an especially large fellow will form from the bones lying on the cavern floor. Take him out with fire attacks or careful swordplay, then investigate the tomb that he was guarding to pick up the Darkmoon Seance Ring. It's an important item. Once you have it, knock out a side wall in that passage and head up a series of stairs to find one of the stage's necromancers and some skeletons. Take them out and then climb the ladder to reach a high secret room. You'll obtain the Tranquil Walk of Peace miracle from a corpse you find at the end of that passage, just past a trap statue. Then you should check the floor for a week point where you can drop through to an earlier portion of the stage.

Return to the portion of the stage where you descended along the spiral staircase in the vertical shaft and make your way through the new opening that appeared after you pressed the switch. When you proceed in that direction, you'll almost immediately come to a split in the path. The path straight ahead is presently useless because of some upturned spikes, so take a detour left through a dark passage to find a trail that leads left along the side of a cliff. Follow it to the apparent end and you'll find a statue that bristles with spikes, as well as a ladder to your right. Roll past the statue and against the wall to reveal a hidden opening. Beyond the opening are some stairs that you can climb to a secret bonfire. It's the one that you may have noticed through the wall earlier in the dungeon.

Descend the stairs from a bonfire and now you should climb the ladder that you saw. At the top, there's another large pedestal with a switch. Push the switch to rotate a nearby bridge so that the spikes are no longer protruding upward. Now head back the way you came. You can cross the bridge to enter a mist-shrouded doorway. Note that as you head along the bridge, you can jump over to an outcropping ledge to find the Great Scythe resting on a corpse in a chamber. Make sure not to miss that weapon if it interests you. Then work your way back around and pass through the mist-covered doorway referenced above.
From that doorway, start down along some stairs to the left. Continue descending through the area, battling skeletons, as the path wraps its way around and back toward the right. You can enter the doorway that you find there, or you can take another detour and drop along some ledges to find the Large Soul of a Nameless Soldier on one ledge and the Priest's Hat, the Holy Robe, the Traveling Gloves, the Holy Trousers and the Mace on a lower ledge. This is a one-way excursion and takes you down to the area just ahead of the boss, so you'll probably die and have to return to where you decided to drop instead of entering the doorway. On your second visit, enter the doorway.
Here, you'll find yourself wandering along a narrow, lengthy passage with plenty of skeletons for company. Stone coffins rest on shelves to either side. Continue forward, battling skeletons but not wasting too much time on them because an unseen necromancer will periodically revive them. The path will eventually widen, and as you keep moving forward you'll find a tough enemy (like the one that you may recognize from the room below the blacksmith in the Undead Parish). As always, you should keep a distance while fighting this guy (when possible) and hit him with fire magic. When you defeat him, he drops the usual Demon Titanite and then you can check a corpse behind him to find an Eye of Death.

Turn around and head back the way you came, watch along the wall to the right and you'll notice a coffin extending from it, with the lid ajar. You can get near to the coffin and investigate for a prompt that lets you “nestle” in the coffin. Climb inside and wait for around 20 or 30 seconds. You'll be taken to a secret portion of an area known as the Tomb of the Giants.
Once you arrive in the Tomb of the Giants by way of the coffin nap, head forward and against the back wall, you'll see a huge coffin. You can get near it and pray to the lord of the sarcophagus to enter the covenant. If you do, you'll receive the Gravelord Sword and the Gravelord Sword Dance miracle. You can offer Eye of Death items to increase your stature within the covenant. When you're ready to leave this chamber, just return to the coffin and nestle in it again. You'll appear back within the Catacombs.
As you head back the way you came through the area with the coffins, watch to the left to spot a hole in the wall. You can pass through that hole to find a tall vertical chamber with a ladder. Defeat any skeletons, check the corpse at the top of the ladder for a Large Soul of a Nameless Soldier, then descend the ladder. In the room below, there's a weak floor on either side of the coffin. Defeat any skeletons, then drop through the hole to reach a chamber below where a black knight is waiting.
Take out the black knight with the attacks you favor, then check the nearby corpse that is resting on the nearby ledge for a Soul of a Proud Knight. You can drop from that ledge to reach a lower area.
In that lower area, you'll face a number of pinwheel skeletons that cartwheel crazily around the area. They roll around in a hurry and crash into you, causing moderate damage. The problem is that there are a bunch of the skeletons and they move quickly, plus they are frequently revived by a necromancer you can't see.
From where you drop after battling the knight, head sharply right and look against that door. You should find a path you can follow. Do so and it comes to a 'T' in a brick room. There will be some more skeletons here, as well as the necromancer. Take out the necromancer and the skeletons, then check around and you'll find a ladder that you can climb. You can either head back in the direction of the pinwheel skeletons and defeat them to continue along the cavern area and find the mist-shrouded doorway that leads to the area boss, or you can climb the ladder.
If you climb the ladder, you'll arrive back in the upper area that you've already explored. That may be worth doing if you're running low on healing items. Otherwise, it's time to go face the boss.
Pinwheel
When you enter Pinwheel's area, you're on a trail leading down to a large coffin. Drop through the opening and you'll land in a shallow pool of water as a scene commences. When the scene concludes, Pinwheel attacks.
The first thing Pinwheel is likely to do is send a huge ball of magic your way. Roll out of its path, then head forward toward Pinwheel as he splits into multiple figures. None of these figures are particularly powerful and they'll fall easily to powerful weapon strikes, but they'll also keep splitting throughout the fight as you whittle away Pinwheel's life meter.
Try to keep moving if you want to survive, and have your shield up to block magic attacks. If you have gear such as the Crest Shield equipped, that's going to work to your benefit. Pinwheel's multiple forms like to try to hit you in the back with magic, but if you should still focus on taking them down one at a time. If you're having trouble harming one of the two (they do dance out of the way and one always seems to be more vulnerable than the other), just switch targets and keep up the attack. As long as you brought a few estus flasks, you'll have little reason to fear.
Defeating Pinwheel earns you 6000 souls. He will also drop the Mask of the Child and the Rite of Kindling. The latter makes it possible to kindle bonfires more than you previously could, which is sure to come in handy throughout the remainder of your adventure.
When you're done in the lower coffin area where you fought Pinwheel, head to the back corner and you'll find a ladder that you can climb to reach the top of the coffin. There, you can climb yet another ladder and you'll arrive on the edge of a dark path with light points floating along it ahead of you. Follow the points of light forward on the trail and you'll arrive in the Tomb of the Giants area, if you're ready (though it's unlikely that you are).
If you'd rather head back through the Catacombs and seek out other adventures (which is the case if you haven't cleared the Abyss area yet), head around to the left and you'll find a trail that you can follow to reach a high ledge overlooking an early portion of the Catacombs. You can obtain the Large Soul of a Proud Warrior from the edge of a ledge, then drop down and backtrack along the trail to a convenient bonfire.