In the room with the two green soldiers, go up the stairs and take the narrow bridge up, then exit at the top right of the screen. Follow the path to the next screen and jump off the ledge, hitting the blue soldier off the edge if you want. Continue up until you reach the first floor.
Exit right and go down the narrow hallway, defeating the green soldiers again, exit south and then exit through the door in the west wall. Zelda will tell you to go to the throne room to find a passage leading to the Sanctuary. Go up the stairs near you and find the door in the north wall, and go through.
Quickly walk up the stairs to avoid a fight with the blue soldiers, and continue north until you reach the thrones. There's an ornamental shelf behind them. Zelda asks if you have a lamp, then says to push the shelf from the left. Note that if you never picked up the lamp along the way, you won't be able to push the shelf, and you'll have to go back to Zelda's cell to get the lamp!
If you're all set, push it from the left until it stops, then go through the door that's revealed.
In this dark room, watch carefully for rats. Note that rats carry a lot of rupees, so you should try to kill them all to collect a lot of cash.
A little above you is a path to the left, at the end of which is a pot hiding a magic jar. Leave this small hallway and go up to a couple of pots, one hiding a magic jar and the other a rupee. Then head right, through another path. The path turns north and there is a pot hiding a heart. Continue up to a stairway leading down.
In this hallway there are ropes (snakes) coming from the left, so do your best to hack them to bits and continue on down the stairs.
More ropes, and now some keese (bats) that will fly if you get close. Cautiously head left to a pot hiding a magic jar, then head right to a chest containing a key. Now go back to the center and north to the locked door, and go through.
Zelda announces that you're now in the sewers (ewww) and are close to the Sanctuary. First go straight up but stay in the water to find a bunch of rats swarming around. If you're standing in the water they can't hurt you, but you can hurt them, so this is a chance to get a bunch of rupees. Kill all the rats that come circling around the edge, and collect the rupees they leave behind.
From here head left. There should be a single rat on a small platform in the water, kill it to hopefully get another rupee. Then continue left and exit through the door here.
In this room there are pots hiding magic jars and hearts around the bottom and left side of the room. The exit, surrounded by two keese, is in the top middle. Kill the keese if they get in your way, and exit north.
In this room, walk left and kill the rats in this area. One of the rats to the left should leave behind a key, though that rat might move to the right. In any case, kill the rats until you find the key, then head right, kill the keese, and continue on through the locked door.
Finally, some light. Kill the rats around here. You'll see some cracked walls to the left, but you can't open them now, so just ignore them. Get rid of the keese in this room, then head north to find a block puzzle. It's really easy, just push the top middle block up and continue up the stairs.
In this wooden room, face left and kill the rats that attack from that direction. The pots don't hide any items. Kill the remaining rats, then go through the door below.
Zelda tells you to pull the switch "over there" but doesn't tell you which one. The correct switch is on the right. The one on the left will cause ropes (snakes) to fall from the ceiling, so don't pull that one. Kill the rats. When you get close to the switch on the right, Zelda tells you how to pull it (walk up to it and hold A, then press down). Do it, and the door to the Sanctuary opens. Go through.