Although there is a sort of boss, this is not exactly a full dungeon. It's really creepy, but the temple after this is even creepier.
You should switch to the Hylian Shield, because there are fire keese here that might destroy your Deku Shield.
Crawl through the hole and climb down the ladder. Kill the skulltula, then walk through the wall next to the skeleton. It's an ILLUSION!
Out here, go past the pool of water and follow the shallow water around the room in either direction. Be careful of the skulltula in the northwest corner, and be careful of the green bubble flying around. It flies counterclockwise around the room. Use your boomerang to stun it and slingshot to kill it. Eventually, after going around the shallow water around the room, you reach a Triforce symbol on the floor near a creepy stone mouth pouring out weird-looking water. Play Zelda's Lullaby and all of the water will drain.
Return to the pool of water near where you entered this big room. Now that it's drained you can hop into it (or climb down; there are vines on one side.) The chest in here has some bombs. Crawl through the hole in one side. At the other end, kill the skulltula and climb up and go through the door.
Let yourself get grabbed by one of the gross disembodied hands coming out of the floor. A disgusting creature with a big mouth, sunken pits for eyes, and stubs for arms comes out of the floor. Lock onto it, then wiggle the control stick and tap all the buttons to get free of the gross hand (make sure you jump away from the other hands.) When Dead Hand gets near, slash its horrible face with your sword until it disappears into the ground. You have to let yourself get grabbed by another hand to make the monster reappear, so do that, and repeat the process until Dead Hand collapses to the floor and starts twitching, meaning it's really finally dead and not just "dead".
Under the Well
With that terrifying monster finally gone, a chest appears. Get what's inside: the Lens of Truth. Remember that illusory wall you walked through earlier? When you use the lens of truth, any illusions are shown in their true light. Walls that are not walls will disappear. Invisible monsters will show up. It takes magic to "see the truth," so use it sparingly. You shouldn't have to use it that much here in the well if you follow the walkthrough.
Speaking of illusions, there's an invisible chest hidden behind the one you got the lens of truth from, containing a gold rupee worth 200 rupees. Make sure that you have room for it in your wallet so that you don't waste it.
Return to the main room.
Let's go around and collect a couple of keys first. Once you've climbed out of the hole where the water used to be, you see an area of the central wall to the left that sticks out. The wall here is actually an illusion, so you can walk right through it into a small room with a chest containing a small key. If you have trouble finding it, use the lens of truth. Leave here, then turn left, go straight along the drained path, turn the corner and stop. The wall to your left is an illusion, too, leading to another small room with a small key.
One last key. From this small room, exit and turn right, go straight, turn right again and STOP. Use the lens of truth to see part of the wall to the right disappear. Walk through it and notice a hole in the floor. You can only see it with the lens of truth, so if you turn off the lens, be careful not to fall down it. Carefully open the chest for the compass, then leave the room through the wall that you came through.
Turn right, and go through the passage to the left, and climb down. The chest contains a recovery heart. Then go up and go through the door. Play Sun's Song to freeze the Gibdo and kill it. In this room are a bunch of caskets, and one of them, at the back of the room on the left side, contains a key. To open the casket you need to light the torch next to it. If you have any Deku Sticks, use one to light the torch by that casket and get the key. Kill the keese that come out. The other caskets mostly contain monsters. If you use Din's Fire to light the torch instead, keep in mind that this will make all of the caskets open at once, so you will have to fight a bunch of monsters before you can get the key.
Leave the room the way that you came in. Back in the central room, go straight ahead through the wall in front of you. Be careful of the center of the room, because there's an invisible skulltula AND a hole beneath it. Unlock the nearest door. Inside is a deku baba, and the pots will fly at you and hurt you if they hit you. Kill the gold skulltula in here for the token.
Go back to the center room, and avoid the middle of the room and go to the next locked door. Turn on the lens of truth to see that there is an invisible ledge around the edge of the room. Get around and get this gold skulltula, then leave the room.
Take a left and walk through the wall here. Take another left but turn on the lens of truth. There's a hole in the floor straight ahead under the creepy portrait thing. You want to make a right at the hole, then crawl through the crawlspace to a locked door. Go through and turn on the lens of truth because there are three big holes in the floor and you don't want to fall. Defeat the keese and bomb the beamos. The chest contains 5 rupees. Then go through to the other exit. Be REALLY careful because there is a Like Like in here, so carefully kill it. (I recommend using the slingshot so that you can avoid getting near it.) Then kill the gold skulltula; that's the last one in the well! The chest here also contains 5 rupees.
If you want the map, return to the last room and drop down one of the holes. (If you don't want the map, just leave the dungeon; there's nothing left to do here.) In this basement, follow the passage and bomb the boulders to get out. Go straight and then make a left, and bomb the boulders here. Kill the ReDead and get the map.
To get out of here, you need to collect the three silver rupees over the evil green pond (you can see the remains of other fools who dared to venture into the well) and once you've obtained those three, climb up the ladder for the last two. The way will open. Go through, then go through the wall in here to get to the main area once again. Now you can finally leave this creepy place. (I don't know what the other chests in here contain. Probably just more rupees. Go around and get them if you want.)
There are some other things you can take care of while you're in the past, but you might as well wait until the next time we go to the past. Return to the Temple of Time with the Prelude of Light and pull out the Master Sword once more. If you already went to Kakariko as adult Link and learned the Nocturne of Shadow, use it. Otherwise, go to Kakariko to see the cutscene and learn it.
Once you've played the warp song, you will be looking down at the graveyard from a gate. Turn around and there are stairs going down, so go down. Stand on the little platform in the center and get right in the middle and use Din's Fire. If you did it correctly, all of the torches will be lit and the creepy door will slowly rise. Go through.