Dark Souls

To acquire the Art of Abysswalking, you need to defeat the great wolf Sif, who is located in the Darkroot Garden. You can buy the Astoria seal from the Undead Parish blacksmith to unlock the large sealed door guarding the area. Alternatively, you can go around the back, and follow the shoreline that harbors the Hydra (Near the giants, and the Havel tower). Sif is located just past the Forest Hunter covenant.

You can enter the Darkroot Garden area, through the large doorway adjacent to the Undead Parish blacksmith. The area is guarded by a Titanium Demon.

Strategy on defeating Sif:
It is a good idea to bring a shield to this fight; With enough endurance, all of Sif's sword attacks can be blocked. The generally accepted strategy for defeating Sif, is to stay under his stomach, and strike when you are safe from his sword attacks. Like most bosses, you just need learn the patterns, and the rest will come with practice. Good luck.


Where to use the abyss ring:
The abyss ring is used to enter the domain of the the Four Kings, near the end of the New Londo Ruins area. In the area filled with Dark-Wraiths (big black-armored knights), you will find a white gate that takes you to a spiral staircase, leading down into a pitch black oblivion. If you don't have the abyss ring equipped while descending, you will die. When you have the ring equipped, you will fall into the abyss, but you will survive. The fall, at least.

If you aren't good at fighting Sif and you just need to pass this part of the game through cheap means:

Have a long bow, and buy 99 poison arrows from a vendor (I used the lady in the grate by the Depths entrance, near the Undead Burg). You'll need about 10,000 souls for this. If you need souls, do the Hellkite Dragon farming if you haven't killed him yet.

Go into the fight, and either get killed or save and quit. If you die, go back to the door. If you saved, you should be outside of it. Sif is now aggro'd and is ready to fight. Now, roll to the left of the white fog door and jump up on to the crumbled wall. Keep rolling until you can see him through the wall/trees. Then, shoot 7-8 poison arrows at him until the counter starts to go up on its own. After this, even with lowest damage (1-3 points) it'll keep going up to about 500-550dmg. Then you repeat. You'll have to do this 7 times on lowest damage, so make sure you have at LEAST 60 poison arrows on you. This will take awhile, probably 20 minutes at least. Once he dies the fog goes away. Make sure to run in behind the grave and grab the Hornet Ring.

Good luck!

Another method to try is to equip all soul arrow and fireball spells you have, lock on and stay moving, when he jumps in for a strike he generally stays on the spot so dodge the attack and hit him then rinse and repeat. If you do get hit you can heal instead of attacking.
This may take a shade longer than melee but I did it first time I tried using this approach (after a few melee deaths of course).

EDIT: After I wrote this I noticed my page has yet to be updated and still shows it "not won", apologies.

Another great strategy for defeating Sif is to use a bleed weapon. I was using a +3 Jagged Ghost Blade which can be obtained from a Ghost in the New Londo Ruins (Rare weapon drop, my item discovery was 210 when I received mine).

Just try to stay under Sif's belly and keep attacking (every 3 or so consecutive attacks will cause bleed damage). When Sif jumps back just keep your distance until he starts to do his swiping attack. When he is almost finished attacking, run towards him and roll under his belly and continue attacking. Using your sword with two hands while attacking will speed the process up as well.

Finally, if you have the Dark Wood Grain Ring (can be obtained by killing Shiva of the East's Ninja body guard) dodging Sif's attacks can be made a little easier.