Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
Northern Undead Asylum
You begin in a prison cell. After a body drops down from a hole in the ceiling, you are granted control of your character. Head forward and pillage the corpse to obtain the Dungeon Cell Key. Use it on the nearby door. Now start down the adjoining corridor. As you advance, there are points along the floor that look like scratches with red light oozing from them. You can investigate those points for a rundown of the controls.
At the end of the corridor, stairs lead down into a lower room where you can target a figure who is standing against the far wall. To the right from there, a short passage leads to the base of a ladder. Climb the ladder and exit the small chamber to arrive in a small courtyard. Start forward and there's a sword protruding from the ground. This is your first opportunity to light a bonfire. You'll learn to cherish such opportunities later in the quest. For now, light the bonfire and then start forward again. Climb some stairs and start forward through a chamber. You'll come under attack by a monster known as the Asylum Demon.
Your only goal here is to get away from the beast. It moves slow and slams the ground with a powerful weapon. You can head to one side of the room and dash along it (through some pots) and find an opening on the back left side. When you pass through the opening, bars slam down behind you and provide a barrier between you and the creature (who probably couldn't have fit through the door, anyway).
Descend the stairs and continue forward to find another place where you can light a bonfire. Do so, then descend some short steps. There's a note on the floor instructing you to get a shield. As you start along the next hallway, note the archer at the far end. He'll fire arrows at you, which you can easily avoid with a step to either side. As you start along the hallway, though, watch to your left. There's a slumped over corpse to the side. You can pillage that corpse to obtain the Cracked Round Shield, which you should immediately equip. In the same general vicinity, you can also find another weapon on a corpse.
After you've looted everything, continue along the corridor and rush up to the archer. He may retreat and you can follow and hack him apart with your weapon. Then ascend the stairs that he was guarding and you'll arrive at a wall of mist. Investigate it and step through into the next chamber.
Follow the passage left to a ledge overlooking a large room. The left branch that you can take here is a dead end. There's a hint on the ground with instructions on how you can step back, which you are welcome to keep in mind as you start along the passage toward the right. There, you'll find a split in the path where you can head up some steps or down some other steps.
Cautiously, start up the stairs and you should hear some movement. As you do, dodge quickly to the side. A boulder will roll down the path and damage you if you're standing in the way. After you dodge it, run up the steps and kill the fellow at the top of the stairs who rolled it toward you. Then descend the stairs and look at the wall. The ball will have crashed through it and you can enter the opening to find a hidden chamber. There, talk to the soldier on the floor and listen to his story. You'll be rewarded with five of the Estus Flask. It's an Undead favorite. You'll also receive the Undead Asylum F2 East Key, which is sure to come in handy.
Head back through the opening now and descend the stairs in the previous room. At the base of the stairs, look left to find a door through which you can pass. The opening leads out into the familiar courtyard where you can rest at a bonfire again. Then climb back up the stairs you just descended. Return to the area where the enemy rolled a boulder down the steps to try and crush you. The enemy will have returned if you rested at the bonfire, so kill him as necessary. Then use the key that you obtained from the soldier to open the door.
Continue along the corridor and there are more hints on the ground about kick attacks and two-handed weapon wielding. Beyond those, the passage opens into a wider area where you can investigate a corpse to obtain the Pyromancy Flame. Nearby, there are two skeletal enemies that will try to hack you apart while beyond them, an archer waits. If you try to take out those soldiers without paying attention to the archer, he'll pelt you with shots from a distance. Lure the skeletons toward you so that they round the corner and you have less issues to deal with at once. Eliminate the skeletons, then head beyond them and tend to the archer.
Ahead of and to the left of the archer's standard position, there's a wall of gray mist. You can pass through it, or you can head through an opening beyond the archer's corpse to find a room with an armored knight. You can prevent him from being an issue if you target him and then take him out with projectile magic before he gets near. Otherwise, parrying and riposte moves will prove necessary.
Behind the armored soldier is a locked door. You can't open it yet, so you'll need to backtrack to the wall of mist that you saw previously. When you pass through it, note that you'll immediately find yourself in the chamber patrolled by the Asylum Demon (the monster that you ran from earlier in the stage). Defeating him is your only way forward.
The Asylum Demon is a huge monster who you very possibly can't see as you first enter the chamber. That's because he's stomping around far below you. However, that doesn't mean that you're safe. If you stand where you are on the ledge that grants entry to the room, he'll leap up and destroy the ledge, inflicting serious damage on you in the process. You'll die. It's not pleasant.
To win the fight, you need to take the offensive. Jump from the ledge and brandish your sword or other such weapon as you plummet toward the ground below. With any luck, you'll land a fearsome blow that cuts away half of his health. Then you'll find himself standing nearby. The first thing you need to do, of course, is roll away so that he can't just immediately hit you with his massive spiked club. Then from a distance, target him with projectile weapons or move in close and hit him with melee attacks from the flank if you must. The demon may be halfway gone, but he'll still put up a fight.
As you battle, make sure that you roll away from his attacks. You can withstand a knock or two from the club, but once you take a hit it's easy to let yourself get cornered by the pillars or pots and then it's difficult to avoid taking additional damage. Try to keep moving and stay out of the range of his club as you plan and execute each attack. Once you hit him a few times, the fight concludes.
Once you defeat the Asylum Demon, you'll receive the Big Pilgrim's Key as your reward (along with a bunch of souls). The double doors that lead to the courtyard with the bonfire will open, so you may want to use that resource before you proceed. Then you should head along the chamber where you fought the demon.
On its far side of the chamber, there's a set of iron doors. You can open them with your new key and you'll arrive on a grassy trail. A hint on the ground congratulates you and instructs you to continue straight ahead. You're safe to do so. Just walk along the grassy path to the end of the cliff and you'll trigger a cutscene as you finally are allowed to leave the shrine and begin your proper adventure in Lordran.