The Skull labyrinth got its name because, once you possess the map the entire layout looks like a skull.  There are 6 hidden passages in the labyrinth labeled A-F.  Out all these passages, take all letters in order except Passage C (which must be skipped because it takes you nowhere).  There is only one passage you will travel twice, Passage D (which is used to get the Silver Arrow and then return, so you can kill Gannon).

The dungeon has Lammolas (The Wand/Book combo works real well on these creatures), Partas, Wizzrobes, Zols, Gels, Keeses, Vires, Pols Voice, Like Likes, and finally Gannon.

Before entering this labyrinth, have the Red Medicine bottle, and at least 90 rupies just in case you must leave for more Medicine and/or to buy another Magical Shield.

Once in the front room, you must go north.  In that door, if you got all 8 triforce fragments, the shutterdoors will open.  If you do not, a old man will appear saying that you may not enter the place.

Continue north from that room.  Now bomb the west wall in that room and go through that newly-created door.  Use the magic wand (if you got it) to wipe out the Lamolas.  When that is done, open the passage.  On the other side of the passage, keep going east until the room with a Parta (should be in the second room from where you emerge).  From that room, go south one room and bomb the east wall in that room.  There, a door will show up.  Go through that door and a Parta will be waiting for you.  Wipe out the Parta (you must destroy the outer part before you can kill the inner part, and the only method is with the sword).  Once the Parta is destroyed, get the map.  Now plant a bomb in the north wall and go north.  Plant another bomb in the north wall in that room for a secret room.

In the secret room (which should be A-16 on your grid), knock off all the wizzrobes and open the passage for the Red Ring.  Now your defense should increase by another 1/4.

Now return to the room where you saw the first Parta.  This time, destroy that creature and the north door will open.  In that room, there is a message saying "Go to the Next Room".  Bomb the west wall and open the passage in that room.

When Link emerges in the other side of the passage, Link should go west two rooms until he sees yet another passage.  Take that passage -- Link will emerge on C1.  Bomb the north wall for a door.  Now wipe out all the Wizzrobes and Like Likes for the Silver Arrow.

Now return to the passage and take it back to G2.  Here, go north two rooms.  When you take care of the Like-Likes and Zols, plant a bomb in the west wall and go through that door.  Now wipe out all the enemies and open up the passage.

This passage should take you to the second room south of the left eye.  That room has Parta.  Kill the Parta to open the shutterdoor.  Now use a bottle of medicine to ensure that Link has full life, and then equip with the Silver Arrow.

Go north through that door, and Gannon will appear.  Although Gannon is invisible, his fireballs and the black tiles in the room will tell Link where Gannon is.  Just keep striking away with the Magic Sword.  If Link hits Gannon, Gannon will appear briefly.  It takes 4 sword strikes with the Magical Sword -- on the fourth successful strike, Gannon will stop and turn red.  Now use the Silver Arrow to complete the job.  Gannon will turn to dust.  Take the Triforce Power and the north shutterdoor will open.

Extinguish the flames with the Magical Sword, and Princess Zelda will await you.  That's the end of the first quest, and all subsequential quests with your character will be under the "second quest".

Note: did I confuse you in this section?  I have made a map detailing the route you must take.  There are 57 rooms in this dungeon.  You only need to visit 26 rooms in order to clear this level and save Zelda.