Hyrule Castle:

Talk to the guard, and move back and forth between the Market and the castle grounds until you see a girl standing by some vines on the side of the path.  Talk to her until she give you an egg.  Now climb up the vines and jump over the gate the guard was guarding.  Move along the path until you see two guards up ahead of you...don't go near them!  Instead, go left up onto the hill.  Watch out for the guard on the hill, run behind him and head to the far left toward a cliff.  You should see some climbable rocks on the cliff, climb them and then jump off the other side toward the castle.  Jump into the moat and swim down it until you reach the corner where you can safely climb out.  Follow the path around and you'll see the sleeping Talon.  Wait until your egg hatches in the morning and use it on Talon to wake him up and get him out of your way.  Once he's gone push and pull the blocks to dump them in the moat.  Use them to jump across to where the water comes in and climb through the hole there.  Now avoid all the guards by not letting them see you and make your way to Princess Zelda.  Talk to the princess.

Lon Lon Ranch:

Head to Lon-Lon Ranch in the middle of Hyrule Field after the story sequence with the princess is over.  Go into the first door on your left and talk to Talon.  Play his game until you win and you'll get a bottle of milk.  The milk is sort of useful but the really useful thing is the bottle itself.  Also, go to the horse corral and talk to Malon until she talks about a song her mother composed.  Whip out
your Ocarina and she'll teach you Epona's song.  Now leave Lon Lon Ranch and head back to Kokiri Forest.

Lost Woods:

Once in Kokiri Forest, climb up the vines behind Mido's house and go through the hollow log to get to the Lost Woods.  In the lost woods, follow the sound of the music (wherever it is loudest) to get to the sacred forest meadow.  For lazy people, the directions are R,L,R,L,F,L,R.  Then kill the wolf, enter the gate, navigate the maze, and go up the steps to get to the Meadow.  Talk to Saria to learn Saria's Song.  Now head back out of the woods and leave Kokiri Forest.  Head to Kakariko Village now.

Kakariko Village:

Explore the town and get the various items available to you at this time.  The most important things to get are the Hylian Shield from the graveyard (See section 1), the second bottle (See section 2), and the Song of the Sun (See section 6).  Once you've got what you need, talk to the guard at the North part of town and show him Zelda's letter.  Don't listen to him about buying a shield...you can find one for free in the graveyard.  He'll talk about wanting a mask which you can now go and get from the Happy Mask Shop in the market.  If you wish you can now do most of Young Link's Trading Sequence.  Go past the guard and head up Death Mountain until you find Goron City.