Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
You'll find the trail that descends into Darkroot Basin along the edge of Darkroot Garden near the blacksmith in Undead Parish. If you start from the smith and head along the trail, there's a sharp right you can take after the first root monster attacks you. There, you'll find a glowing flower. You can head around behind it and descend along a precarious ledge that leads into the basin.
You can descend along the trail for some distance and then ahead of you, you'll see a glowing enemy. It's a rare lizard that drops a valuable item if defeated, so try to take it out swiftly before it has time to run away from you. Then continue your descent. The trail will double back on itself and you'll see two paths descending ahead of you. One descends less steeply than the other. Head along it to a wide ledge, then drop to a lower ledge and check the corpse to obtain the Leather Armor, Leather Gloves, Leather Boots, Longbow and sixteen of the Feather Arrow. Then drop down again and now you're on the trail you saw descending more steeply.
As you continue along the trail from there, you'll reach another split in the path. Here, you can head either left or right along a precipice. Wide trails lead in both directions.
Start with the area to the right. Proceed cautiously, though, because you'll face one of the black knights. Hit him from fire with a distance, if possible. Then when he's defeated, grab the Blue Titanite Chunk that he drops and descend the trail to find a corpse resting at the end. Loot it for the Grass Crest Shield, then start back uphill. As you do, you'll notice an opening where you can head into the cliff. If you head up through that opening, you'll find a bonfire. Beyond that bonfire, there's a lever that you can pull to activate an elevator.
The elevator leads to an area known as the Valley of the Drakes. You can head there, of course, but you still have business in Darkroot Basin that you may wish to tend to first.
Return to the overhead ledge where you had gone right at the fork in the trail. This time, you'll want to proceed along the left route, which is straight ahead of you as you approach it now after ascending from the bonfire. Along that route, you'll reach a much wider area. As you look ahead, you'll see white giants made out of crystal. There are around four of them, positioned along the sloping hills ahead of a large body of water.
Manage your approach by heading forward along the left side of the area, along the higher ledge. Move forward and you can likely throw firebombs or use fire magic from that vantage point to take down the nearest of the crystal giants. Then you can lure another one toward you. Target them and back up the slope, hitting them with your attacks to easily eliminate each one. Then you should continue forward and lure any others down toward you, one at a time.
After those crystal giants are out of the way, you can head right to find the Large Soul of an Undead Soldier on a corpse, and past that an area where there's a locked door. Use the Watchtower Basement Key on it and you can unlock it, providing a shortcut to Undead Berg (though it's guarded by a fierce warrior).
Spare yourself a moment for that detour and possibly kill the fellow on the stairs (use attacks from behind, and you probably shouldn't risk magic unless it's really powerful). You'll receive Havel's Ring as a reward. When worn, the ring increases the amount of heavy equipment you can easily carry around with you.
Return to where you fought the crystal enemies and proceed toward a shallow lake shore. Near the right side of that lake, you can check a corpse to find the Knight Helm, the Knight Armor, the Knight Gauntlets and the Knight Leggings. The loot is guarded by a hydra, which packs quite a punch unless you have really good defenses. It will try pelting you with projectile attacks and it will sometimes send its heads to the shoreline, which is the place from which you should mount your attack. Let any heads crash down on the shore beside you and hack them off, one at a time. Otherwise, face out to the water and either dodge magical projectiles that the beast fires or block them if you have a capable shield.
When you defeat the monster, you will receive the Dragon Scale and the Dusk Crown Ring. Then you can head left along the shallow lakeshore edge (if you venture too far into the center, the water gets deeper and you'll plunge to your death) and find a ladder. Climb the ladder if you want to reach Darkroot Garden, in the area beyond the sealed gate.
Alternatively, you can exit the area and then return. Proceed to the area where you fought the hydra and advance beyond it to find another of the crystal giants. It is a tougher one than the others, but still shouldn't pose any real problem. Defeat it to free Dusk of Oolacile. Answer “Yes” to her question and you'll be able to summon her when needed. Now you're definitely done in this area and should head elsewhere, perhaps to the Valley of the Drakes.