Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
Undead Burg Slums
When you clear the Undead Parish, you'll need to return to the Undead Burg. Make your way to the area where you battled the Taurus Demon, then descend some steps in the tower that he was guarding. You'll come to the area ahead of the long stone bridge, where the dragon breathes fire from its perch on the distant roof. Ahead of you as you stand at the base of the stairs that you just descended, there's a door. You can use the Basement Key (obtained partway through the Undead Parish) to open it.
Past the door, stairs descend to the top of a ladder. You can descend that ladder and then a series of steps to arrive in an open area. There are some stairs that climb to the upper right. Ascend those stairs and then follow them back to the left to reach a locked door. There are enemies waiting behind the door. Open the door and then roll into the room. Take out the enemies quickly and head toward the far door. You'll see a familiar walkway that leads to a similarly familiar bonfire that you've likely used many times before. Take advantage of it, then return to the door that you just opened.
Descend the stairs that you climbed a short time ago and at the branch in the path, look down along some steps that descend past a massive blaze. You can start down those steps, but only advance to the first landing and then wait. You'll likely attract the attention of one of the hounds that roam this area. They move quickly and are capable of poisoning you, so you don't want to have to deal with more than one at once if you can help it. Stand on the landing and let them approach you. Block their leap with your shield, then counter with a sword swipe.
There are three hounds, so take them out as you see fit and then advance toward where a cart is waiting in the street. You can break it apart or leave it where it is, though presently you may wish to use it for cover. Just past the cart and to the left, there's a doorway. It's locked, and so is one to the right. If you advance along the alley, though, the doors will fling open and three assassins will rush you. They carry poison-tipped daggers. In a group, they're fearsome opponents. Don't let them get behind you or they'll try to slit your throat (perhaps successfully). Be careful to keep your shield up to deflect any daggers they might try to throw, as well. If you didn't break the cart, you can use it for shelter to make it easier to battle only one or two assassins at once.
When you have killed the assassins, you can check the buildings from which they emerged. In the first recently opened building to the right, you can find the Mail Breaker weapon on a corpse. You can also head back toward the blaze but watch to the left. A path in that direction leads past some buildings. You can open the door on one of those buildings to find Griggs of Vinheim, a sorcerer. Talk to him and he'll announce his plans to head back to Firelink Shrine, which is convenient. You can roll through the barrels to the right, as well, to obtain a bunch of loot from a corpse that falls out of one: the Sorcerer Hat, the Sorcerer Cloak, the Sorcerer Gauntlets, the Sorcerer Boots and the Sorcerer's Catalyst. If you head further down that side alley, you can beat a bunch of torch-wielding enemies and investigate a corpse they were guarding to obtain a Twin Humanities item, as well. Then it's time to return to the main path.
Continue along that main path through the burg and you'll find yourself approaching a grassy basin. That grassy area should not be approached too quickly because as you start down the steps, a hound will rush you. Block its attack, then hit back. Slowly start forward again. Check to the left to find a small recess in the wall where a corpse stands upright in a barrel. Break the barrel apart to obtain a Large Soul of a Lost Undead and then return your attention to the area not far ahead.
You'll notice there are huts on either side of the grassy walkway. As you get near enough, enemies will emerge from the huts. Again, let them come to you and hit them with whatever attacks you like. Then investigate the corpse in the second building on the right to find the Thief Mask, the Black Leather Armor, the Black Leather Gloves, the Black Leather Boots and the Target Shield. Note that heading forward may call another of the poisonous hounds to attack, so be ready for that.
Proceeding forward, you'll notice a mist-shrouded archway ahead of you. Through that archway there is a boss encounter, but you're not ready for that just yet. First, you should continue exploring.
To the right of the mist-shrouded door, you'll see stairs that descend in that direction. Head down those and to the first landing, then look ahead of you at the steps that continue their descent. Ahead of you, in plain sight, there waits an enemy. From the landing where you're currently positioned, you can fire an arrow to snipe him. Draw him to you in that manner and take him out, then start forward again but keep an eye on the left wall. As you are most of the way down the stairs, an assassin will attack from a recess there. Be ready for him and hit him with whatever attack you like. Then continue forward toward where you shot the poor fellow near the base of the stairs.
After his corpse, there's a wide alleyway ahead of you. Stairs lead up to a door to the left. You can climb those stairs and then enter a tower with a spiral staircase. Put up your shield and head up the stairs. An archer on an upper platform will try to kill you, but he's easily defeated. Keep climbing from there to the next floor and you'll see an opening ahead of you. Stairs continue to ascend to your left, but permit yourself a detour to the opening and talk to the person behind the bars to the right after passing through that opening. He is a merchant. You can purchase a variety of items from him, including the Purging Stone (his price is steep, though) and precious Humanity. The moss items that he sells can easily be obtained for free by defeating enemies in the Darkroot Garden area, so there's no point in buying them here.
If you head left from where you meet the merchant, down the long tunnel, you can find and open a door. It doesn't require any special key. Opening the door activates a shortcut to Firelink Shrine for possible future use (it's handy if you want an easy route to the nearby boss from a convenient bonfire without having to travel through most of the burg, for instance). Then you should return to exploring Undead Burg.
Continue along the alley and at the end, you'll find a corpse that you can pillage to obtain a Large Soul of a Lost Undead. Just ahead of that, there's a doorway that leads into a room to the right. When you first find that door, it's likely locked, meaning that you've presently explored as much of the area as possible until you defeat the boss. Head back up the stairs to face him now.
You'll find a relatively easy boss waiting in this chamber, along with two of the poisonous hounds. While it's true that the demon is capable of dealing the most damage with his massive swords, you actually have more to fear from the hounds (particularly if two of them corner you at once while you're trying to take down their master). Do yourself a favor and tend to the four-legged critters first before you focus on the main target.
Once it's down to just you and the demon, you'll find that he's not a huge threat. You can block his swings and the worst you'll suffer is some stamina loss. You can get in close and hit him a few times after he misses with a series of swipes. Then you can back away and give yourself some distance if you need to gulp down an estus potion.
There are some high stairs along one side of the room, which is another thing to keep in mind. You can jump from the top of the stairs and slash down on your foe if you get the positioning right, though you may have a simpler time just going up against him the old-fashioned way. Still, the stairs are obviously there for your benefit. Use them as needed and soon you should turn your worthy foe into a less worthy corpse.
When you defeat the Capra Demon, you'll receive the Key to Depths. There's nothing more to do in the chamber where you fought the Capra Demon, so exit and take a sharp left turn to follow some stairs down into the alley that you explored a short time previously. Remember the locked door? You can open it now to reach the next area: Depths.