Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
There are two routes that you might follow to enter Lost Izalith, and the process you follow determines whether or not you can save the NPC named Solaire, or whether you must battle him.
To save him, you'll need to enter Lost Izaleth by a secret route. You must deepen your affinity with the Chaos covenant by handing over enough humanity to reach level 2. This will require handing over 30 humanity without abandoning the covenant, which is most easily done if you farm humanity in the Depths area of the game by defeating rats. Then as you are working through the Demon Ruins, battle until you reach the area ahead of the chamber where you fight the Demon Firesage boss.
To the right ahead of that chamber, there's a hole in the wall with roots growing down along it. You can carefully descend along those roots to reach a sealed doorway. Pass through it and open the door that lies beyond (it won't open if your Chaos covenant level isn't high enough) and start through the corridor. There are nine bug enemies here and you must destroy them all without stepping forward too far and accidentally entering Lost Izaleth. If you fail to kill them all, you'll eventually have to battle Solaire.
If you don't care whether or not you save Solaire, you can take a more conventional route to the Lost Izaleth area. When you reach the bottom of the Demon Ruins, you'll battle the Demon Centipede and obtain the Orange Charred Ring. It allows you to head across lava while receiving reduced damage compared to what you would otherwise receive. You can cross to the left side of the chamber where you battled the demon and proceed onward through a narrow passage to descend into Lost Izalith. Right at the entrance to the area, you'll find a bonfire. If you see Solaire seated nearby, then you've taken the route that means you'll have to eventually kill him (near the end of this area). He'll has gone hollow.
If you followed the path to save Solaire, you'll arrive in Lost Izaleth at a later point. If you don't watch out for Solaire's welfare, your arrival in the earlier portion of the area will find you at the edge of a lake of molten lava. Make sure that you keep the Orange Charred Ring equipped and start along that lake. You can follow tree roots as you go to mostly stay out of the lava. They'll lead you forward and into a wide area, then along the left side as your movement possibly attracts the attention of the massive enemies in this area.
Move around on the limbs and then reach safe ground near a corpse that you can eventually check for the Soul of a Brave Warrior. Before you check, though, let any enemies that have followed you take care of one another with their jump attacks. They are such big foes that they'll often damage or even kill one another, making things easier for you. The best part is that the enemies won't return once dead, even if you return to a bonfire.
Clearing the huge enemies out of the area may take quite some time and a few trips back to the nearest bonfire, but eventually the immediate area should be clear to proceed. Then you can head around (still mostly sticking to the roots) and reach the entrance to a building. Since the monsters around you can't enter this building, you can use it for shelter. Stand inside the door and let foes get near, then sneak out and hit them with your weapons or magic before retreating back into the building and repeating this process. Using that tactic, you should be able to eliminate a few more of the monsters. Make sure that you obtain the Soul of a Great Hero from the treasure chest inside the building, too.
Then it's time to make your way toward the next building. Ahead of it, a huge root dips down into the lava. You can step onto the root and follow it up toward the next building's higher level. Watch out for any enemies that may try to rush you along the way. Rush quickly up the root to the higher ledge that protrudes from the building's left side. Step onto that ledge to find a safe vantage point. If you press near the building there, the monsters can't harm you. Then you can head around and snipe them with long-range projectile weapons. Grab the Twin Humanities item from the corpse on one side of that ledge, as well.
When you're done, you can and should drop down to the lowest level. Check the building walls on the side that overhead has the extended ledge. You can roll through the wall to reveal a hidden room with a bonfire, the last one in this area. Activate it and then you're ready to push through the last bit of the level.
After using the bonfire, head back out and proceed straight ahead through the lava in that direction to reach a stone structure that looks like a partially submerged tin can floating in the lava. As you pass through it, you'll find some roots that you can then climb. They lead up along the wall to the left. Climb to the top of the roots and you'll find yourself overlooking a lower courtyard area. There are many of the statues here that come to life and chase you around breathing fire, so prepare yourself for that and then descend to face them. Keep an ear out for the sound of them breaking free from their casings, and watch around the corner to the left for one that tries to hide and approach when you're distracted.
On the far side of that courtyard, you can pass through one of two halls with a low ceiling. Be careful of the statues that come to life as you pass through, though. On the far side of those tunnels, you'll find more statues in a more open courtyard area. Defeat them and head forward to find some stairs that ascend to the upper right. Walk around the back side of those stairs to find the Large Soul of a Brave Warrior on a corpse. Then climb the stairs.
As you start up the stairs, you'll attract a large enemy near the top. He'll start rolling down to face you. Get close enough to target him, then back away and throw magic or fire at him to eliminate him from a distance. Once he's gone, climb to the top of the stairs and head right through that small square chamber to find more stairs.
The stairs lead in the direction you ultimately need to go, so remember this location. You'll be coming back to it, but first you can choose take a detour to the lower right to experience some important events and to grab some items that will be astonishingly useful in the near future (even though they're not required). You'll find most of the loot and the important event by following a root trail that leads down and to the left into a wide courtyard, while the rest of the items are located at the base of another root further to the right that leads to a ledge that you can circle to find the Soul of a Hero and (once you drop down again to the area you visited a short time ago) a Rare Ring of Sacrifice.
The main vine that leads down into the plaza area should be descended only when you're ready for more of the statues to come to life and attack. There are a lot of them, so try to work your way across the area smartly and not let any sneak behind you. To the left of the area, you'll notice a dark passage with a corpse resting inside. There's a glowing point on the corpse, but that item is a trap to lure you into a dangerous area. Ignore it for now and look to the right instead, where some stairs ascend.
Climb the stairs and you'll find a long walkway. This is the walkway where you will have arrived in the area if you entered by way of the special entrance from the Demon Ruins area. Along the walkway, you'll find one of the headless demons that attacks with a trident and scorpion tail. He's dangerous, as you'd expect, so keep your distance and pelt him with fire attacks as possible to wear him down. Then move in closer and disable him permanently.
Proceed along the passageway and you'll find a crystal lizard that tries to escape you. Defeat it for a nice reward, or it'll just get away and you'll get nothing. Beyond that is an area where small bugs are jumping around. They can't harm you, but you can kill them. Among them, if you didn't save him from his fate, is the familiar form of Solaire. He'll attack you if he's there and you will have to defend yourself from his attacks and then slay him. When you do, check his corpse for the Humanity and the Sunlight Talisman, Iron Helm, Armor of the Sun, Iron Bracelet and Iron Leggings.
While you're in this area, make sure that you kill each of the hopping insects until you beat the one that will drop an important item, the Sunlight Maggot. You can use that item in the Tomb of Giants area to see without the use of a lantern. Such an item is invaluable in that region.
Now head back to the area mentioned previously, where the corpse with an item on it lies on the underside of a tunnel. You're ready to spring that trap now. Inch forward and keep to the left wall as you do so. The brick floor will collapse to your right, but you'll be safe as you stand on a root trail. Descend it toward the lower area and you'll come to a lower ledge where you can step off the trail and head right to the top of some stairs.
You don't want to go down the stairs. Instead, go left and drop down to a lower point, then head through the roots. Keep away from the hole near the center of the floor, but look through it and you'll see several large enemies waiting. They were the trap that was meant to catch you when the floor caved. Now you can take care of them using magic from the upper ledge, or some shots with a bow and arrows. Once the enemies are defeated, you can drop down and check out the area. First, though, equip something to add protection to poison. The water here will leech your defenses and then poison you if you're not careful.
The items you can find in this low area are mostly just titanite chunks of various colors. However, once you have dropped down in the murky soup, you should head around (being careful to walk around the edges of the gaping holes in the floor, which isn't terribly difficult) to find the Red Titanite Slab in a far passage. Then you can head back up the stairs and up the root trails to at last return to the point at the base of the highest staircase where you first took the detour to the right for all of the loot hunting (in other words, the point we said you would be returning to eventually). Now you're ready to finally start up those stairs.
As you ascend the stairs, do so with caution. There may be an enemy waiting to rush you on the steps. If you see him coming, note that he uses powerful pyromancy and is all but impervious to any that you may throw at him. You'll do much better if you dodge his fire bursts, then move in from the side and hit him hard with a melee weapon as he is preparing to cast.
Head up the stairs past where you defeat him and you'll see stairs descending left toward a mist-shrouded doorway. That's the door through which you'll find the area boss, but first you should continue along the upper path and head around to the right. Another enemy waits there, so defeat it with fire attacks or careful melee maneuvering (you don't want to let it suck you up or it'll potentially kill you instantly, depending on your stats). Then head past it to find a treasure chest that you can open to obtain the Chaos Fire Whip. Now backtrack to the mist-shrouded door that you saw and pass through it when you're ready for a boss battle.
Bed of Chaos
This is a challenging and unique battle that you can't win based on your stats (though having a powerful character doesn't hurt). You'll have to rely on ingenuity.
As the fight begins, you'll see what looks like a large tree ahead of you with a bunch of gnarled branches. This is your foe, but you won't try to beat him in a head-on fight. Instead, you'll need to disable two barriers on the far sides of the arena.
Start with the one to your left. You can and should sprint toward it to reduce the amount of time that you're an exposed target for your foe, who will sweep at you with his large limbs. These can be blocked, mostly, but they'll still inflict damage and you need to be in the habit of avoiding them whenever possible.
Once you reach the glowing barrier, you can step through it and then hack at the object behind it, a glowing limb. When you do enough damage, a scene is triggered.
Now you need to head back around the way that you came, toward where you first entered the arena, but running is actually a bad idea now. The floor ahead of you will periodically give way and you'll have to pick your way along the path. Keep your shield up and move slowly, primarily sticking to the points where tree trunks are rising out of the floor (the brickwork near their base won't crumble away like the other will).
Note that while it's possible to head left of the brickwork so that you're on the main pedestal ahead of the tree, that's not recommended because the tree is more easily able to use sweep attacks with an arm that he grew when you destroyed the first barrier. These attacks will knock you back and cause damage, but a bigger concern is that they're also likely to knock you into a bottomless pit. You'll die instantly if that happens, regardless of your life meter.
Make your way around to the starting point, and from there continue right to reach the second of the glowing barriers. Step through it, as well, and destroy the glowing limb. Now the Bed of Chaos will grow a second arm and you'll have to return to the starting point yet again as it gains a new attack that allows it to create eruptions of fire. If you see red glowing on brickwork nearby, steer clear of it to avoid a fiery death.
Head back around to the left and continue to keep to the brickwork rather than getting close where the boss will hit you with his lethal sweep attacks. Look ahead of the starting point and you'll notice that the pedestal has now fallen partially away. Bait and avoid a sweep attack, then rush toward the center of the area and leap to a lower root ledge. Run along that platform now and when you reach the end, you'll see some more branches. Hack them and then continue along the path, hacking more of them. Pause and hold up your shield if fire erupts around you, but otherwise you can't be harmed. Proceed forward to find a corpse lying on the ground.
Attack and destroy the corpse to win the battle. Note that if you do fall in battle, any progress you've made is saved, so you won't have to re-hit the branches behind the barriers and you won't have to make the pit appear at the center of the pedestal. In that respect, the fight isn't so difficult after all.
Once you defeat the Bed of Chaos, you'll receive the Lord Soul. You can light a bonfire that appears where the corpse was lying, then use it to warp out of the area if you like.