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 finally have an opportunity to level up your character now that you've cleared the Northern Undead Asylum. Head to the bonfire and when you access it, you'll see some new options that you'll want to make use of for the game's remainder. Make sure that you level up your character using the souls that you've gleaned thus far.
When you're ready to proceed, talk to the man who is sitting on the nearby steps, among the grass. He'll give you a tip about ringing a bell high in a tower and another one that is far below the surface. Then you should investigate the surrounding area. There are a number of items to find on corpses in the ruins at the top of the steps leading uphill from the bonfire. You can find the Firebomb and the Soul of a Lost Undead. There's also the Humanity that can be obtained from the corpse draped over the edge of the well, nearer to the bonfire. It's also possible to descend a trail left of where the man is sitting on the steps. That path leads to a lift that you can ride to a lower area where a blacksmith is located, but there's really no reason to go there just yet since you don't need his services.
The well at the center of Firelink Shrine is a good marker when you're ready to proceed. Beyond it, against the base of the high rock wall overlooking the area, there's a steep flight of stairs. Head up those stairs and near the top you'll find two swordsmen. Defeat them near the top of the stairs, without heading forward any more than you have to. Then when they're done, you can look forward. There are more stairs leading upward, with an enemy at their top who throws powerful firebombs down at you. On the lower level, there's also an armored soldier near a corpse where you can find another Soul of a Lost Undead. If you try to take him out without tending to the fellow overhead, you may wind up taking a lot of damage. Proceed cautiously.
Once you're ready, climb the stairs and take out the guy who throws the firebombs. There are more enemies on that high ground, so continue along that route and mind your footing. It's possible to step over the side of the ascending trail and fall to your death if you're not careful.
As you reach a high point on that trail, more steps lead to the upper right and a stone walkway. You can climb those and take out the waiting soldier. Just past him is an opening. Ignore it and head along the walkway to its end to find a Soul of a Lost Undead on a corpse. You also have a decision to make at this point. If you like, you can head back down the steps and walk around to the back side of the stone wall. There, a grassy bank allows you to drop to a lower level of the wall. From there, you can head along the edge (there's just barely room to pass around a few stone columns, if you're careful) and find the Ring of Sacrifice on a waiting corpse. Then you can backtrack the way you came and step onto the lower bank near where you found the armored soldier a moment ago.
Whether or not you take that detour, you'll eventually need to return to the high ground and head through the opening in the wall. There, you'll find yourself with a choice: do you go left or right? If you head left, you'll find a giant rat sniffing at a corpse. Kill the rat and investigate the corpse to find another Soul of a Lost Undead. Then return to the right and proceed in that direction. You'll find a scratch on the floor wishing you good luck, then a split in the path. The right fork reaches an immediate dead end at a gate you can't open from your current position. The left path leads up some stairs and into the next area, the Undead Burg.