Eventually, you'll come to a bonfire. Light it. Welcome to Sanctum Walk. From here, you have two paths.
Go down a staircase and collect Old Growth Balm x 1, which temporarily increases strength. Continue ahead, and you'll find a shaft that you don't want to jump down. Return to the bonfire and take the other path. You'll be back.
Around a corner, you'll find an enemy pretending to be sleeping on your left. This is a Sanctum Soldier, an undead enemy you'll become very familiar with. Kill him, avoiding his enormous Sanctum Mace. Continue along the path.
On a hill up in the distance, there are two sleeping soldiers and a standing archer. On your left, there's a glowing triangular object. This is a Switch, and they're everywhere in Crown of the Sunken King. Put your guard up to protect against the archer's arrows, approach and hit the Switch. Be careful not to walk too far beyond it or you risk rousing the sleepers.
Hitting the switch will raise a structure between the archer and sleepers and cause 700 HP worth of damage to the slumbering ones. Sanctum Soldiers carry Estus Flasks, so the longer you wait, the more likely it is that they'll drink and regain some of the health they lost. Dispatch the awoken soldiers then move along the right side of the structure you raised to battle the archer there. Head back to Switch that raised the structure.
Facing the Switch with your back to the bonfire, turn left. Fire a projectile weapon at the Switch on a rock below you, and a slab will raise next to the building to your left (as seen above). Walk of the cliff onto the slab, enter the room on your left, and kill the soldier with the lance and shield. Ascend the stairs to retrieve Poison Bite Ring +1 from a corpse. That winged slithering sound you hear is fresh new monstrosity in Crown of the Sunken King, a sort of combination between a spider and a fly. Kill it, but keep in mind that the long you take to kill it, the more likely it'll begin to exude a cloud of yellow-brown mist that will degrade your weapon. Walk off the ledge beyond the corpse, and you're back on the path from which you came.
Keep the wall on your right and return to where you killed the archer. There are four enemies just out of sight. If they see you, they'll be happy to charge and fire arrows. Stand back where they can't see you and use a projectile weapon to trigger the Switch and raise a structure between them. That will serve as cover so the archers don't attack. Move ahead and lure your enemies out one by one, backing up when one starts to charge. The last thing you want to do is fight them as a group. Once they're dead, pillage the corpse on the opposite side of the structure for Lifegem x 5.
After everyone's dead and the coast is clear, hit the Switch you already hit to lower the platform, and then hit it again and jump on top of it as it rises. Facing the top corner that looks out over the abyss, jump to the adjacent platform where you'll find a body with Dark Quartz Ring +3.
A note about ledges and jumping. Crown of the Sunken King requires you to make many leaps of faith, but the developers at From Software seem to have designed the ledges to be subtly helpful. In almost every case, a corner of platform you're leaping from will jut out at suspicious angle. Walk or jump off at the point, and you're likely to land on solid ground. If you find yourself confused, look out over a corner.
Make your way back to the corpse that had Lifegem x 5 and look down. Hit the switch with a projectile weapon to raise another structure. Walk off ledge to land on the platform you raised and pillage the corpse for a Long Bow + 7. Walk off the corner on your left and fight the soldier with a sword. Follow the path around toward a dead end to fight another soldier, this one with a lance and shield. Follow the path and pillage a corpse with Poison Stone x 1. Turn around and follow the path up a staircase.
Walk off the ledge by the corpse you plundered. Pillage the corpse with Thunder Quartz Ring +3, which increases lightning defense. Walk off that corner of the platform to the path that leads down to Dragon's Sanctum and up to the path from which you came.
Head up a small staircase, turn left and walk through the doorway of a red room. Walk in just a few feet and then run back out toward the steps, careful to avoid the archer at your right. Two spider flies will follow you out. Kill them.
Reenter the red room and pillage a corpse for Goldenfruit balm x 3, an item that temporarily increases faith. You can destroy the red egg sacs in the room with a projectile weapon, but beware of equipment breakage. They do not contain items or offer XP.
If you're facing the corpse in the red room, the door to your left will take you to the building where you picked up the Thunder Quartz Ring. Walk out that door and take an immediate right, walking on the building's ledge. Walk off the end carefully, turn around and pillage a corpse with Old Growth Balm x 3. From here, you can run the the edge of the ledge and jump or use an item to return to the bonfire. If you make the jump, you'll have to contend with two soldiers, and it's best to lure them back to landing where you entered the red room. If you're approaching from the stairs, descend the staircase to lure two soldiers to their deaths. Dispatch the sniper on the ledge with a projectile weapon. Take the path next to the stairs to pillage a corpse with Lightning Urn x 5.
Enter the room to the right of the red, bug-infested room. Hit the Switch right outside of the other door in the room, which will raise a platform making it easier to walk to where the sniper once stood. Hit the Switch at the far right end of the platform where the sniper was to reveal another structure from the building to your left.
Hop down and walk across the path you just created. You'll find yourself in another red room full of egg sacs. Ascend the stairs and stop about halfway. Look up, and you'll see three spider flies on the ceiling. Lock on and take them all out, as well as the one on the ground in the corner of the room.
Through a doorway opposite the staircase, you'll find a corpse with an Elizabeth Mushroom x 1, which restores some spell uses. There's also a sniper looking to catch you unaware, and you can take him out with a projectile weapon. That's all there is in this building, so run and jump out of the second doorway to make your way back to where you came from.