Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
When you initially head to the New Londo Ruins, you'll find that its lower levels are submerged in water. You can use the Key to the Seal (which you obtain from an old man named Ingward once you have cleared the Anor Lando area and obtained the Lordvessel. With the key that you get from the old man in your possession (find Ingward on the rooftop of a building in that area, after climbing a ladder in a chimney), you can head outside of the building and follow some stairs to reach a locked iron door. Use the key to open it, then head around and activate a lever to drain water from the area.
Next, you'll need to battle your way through the lower portion of the New Lando Ruins until you reach a mist-shrouded door. When you pass through that door, you will be unable to return until you either die and appear back at a bonfire, or once you defeat the boss enemy waiting to challenge you in this region.
Equip the Covenant of Artorias, a ring that you receive for defeating the giant wolf Sif in the area of Darkroot Garden that waits beyond the sealed door. When you have the ring equipped, you can descend the spiral staircase and from the bottom you can jump into the black pit beneath you. After falling for awhile, you'll land in an area surrounded by blackness. As you head forward, “The Abyss” will flash on the screen. Not long after that, you'll find yourself in the area boss fight.
You need to move quickly to win this battle. As it begins, you're surrounded by blackness and it can be difficult to even see your opponent. Look around swiftly and find him, then race toward him and try to hit him hard and fast. You want to inflict as much damage as possible before more enemies appear, which they will do periodically.
One problem is that each king you have to defeat is capable of dealing devastating damage. That's why it's so important that you not fight more than one at a time if possible. Hit with a fast enough weapon to quickly eliminate each foe and make sure that you block the vicious sword swings and roll back out of the way of the magic. You'll do better in this fight if you're able to withstand magic damage easily, as the kings are capable of producing aura bursts around them.
Another move the kings have is to occasionally grab you as you stand in front of them. This move is powerful, but it's a problem even if it doesn't kill you just because it takes so long to play out and thus gives more kings time to arrive on the scene. You'll do best in this fight if you can get around to the enemy's flank or attack from behind and minimize the number of moves that he can use against you. Each king that you take out eliminates around a quarter of the overall boss life meter, so you should soon win if you're able to keep the fight moving along at your speed and don't allow yourself to be swarmed by too many kings at once. Starting out with strong pyromancy magic (if you have it) is a good way to get rid of the first king or two and start the fight along the path you need it to follow.
When you defeat the boss, a bonfire will appear. You can use it to warp back to a more friendly bonfire and then resume your adventure.