Open the treasure chest here for a key and collect all the silver rupees to make a bridge.  Now go back into the first room again and this time climb through the small hole (not the one you came in through, the one between the two torches).  Go through the locked door.  Kill the skulltulas and climb up the wall.

Now you're on floor 2.  Go in the room a ways and you'll have to fight two of those lizard guard guys.  Use your boomerang to hit the shock switch above you and open the chests that appear.  One has Bombchu's in it, the other a Deku Shield or 5 rupees.  Aim a Bombchu so it climbs up the wall and hits the boulder up there.  This will open the doorway.  Go through and look to your left.  Push the stone statue you see straight off the ledge onto a switch.  Climb the steps in front of you to get to a torch and a door.  Light a Deku stick with the torch, drop down, and light the two torches in front of the big statue to get the Map.  Go back to the small statue, climb the wall, and go up the steps again, this time going through the door.  Go around to the next door, and you're now in another silver rupee-collecting room.  You'll have to kill the laser eye guys with bombs or bombchu's to get up to most of them.  After getting them all a torch will light.  Use it to light the other torches to get a chest with a key.  Now move those blocks in the middle of the room around until the one with the sun symbol on it is in the sunlight coming in from the window.  Go through the door that opened, up the stairs, and into the next room.  Go up to that big metal thing sitting in the throne and hit it with your sword.  Now you'll be up against an Iron Knuckle.

This guy isn't all that tough.  If you get hit though, you're in for some serious pain.  Just Z-target and go to right outside his attack range.  Then Jump attack (push A) and you'll get off a good hit and the swing he takes at you will miss.  Back off and then do it again.  If he hits a pillar it will give up 3 hearts.  You can also try getting in behind him when he misses a swing if you're good.  After a bunch of hits he'll be dead.  Go through the door that opens and up a ramp and you'll end up...outside.  Open the chest there to get the Silver Gauntlets.  Watch the story sequence then play the Prelude of Light to go to the Temple of Time.  Get the Mater Sword to become adult Link. Now you have a choice between continuing the Spirit Temple or using your new Silver Gauntlets to go get the Ice Arrows in the Gerudo Training Ground.  If you want to continue the Spirit Temple
skip down to Spirit Temple part 2, adult Link below.

Gerudo Training Ground

Go to Gerudo Fortress and talk to the lady in white clothing outside a blocked door.  Pay her 10 rupees to get into the training grounds.  Once you're inside, turn right and go inside the lion's mouth.  Quickly kill all the enemies in this room to get a key.  Go through the door that became unblocked.  Equip your hover boots.  This part may take some practice and you have to be quick. I've been told that if you play the Song of Time two blue blocks will appear that will make it a little easier to navigate.