Outside Hyrule Castle
You can't enter through the gates because they're closed and guards are
everywhere, so you're going to sneak in! First, climb the wall with vines on
it and run across until you're at the other side of the gate below. Then,
drop down and purposely get yourself caught by one of the guards standing
around. When you're back outside, go back to the wall with the vines and
Malon will be there. Speak with Malon to get a Weird Egg, then climb the
wall. Run across to the gate and go down the ladder and exit the door to get
past it.
Now the tricky part is avoiding the guards, and I'll try and describe how to
get past them as good as I can. When the path turns left for the first time,
run up the hill and into the grassy area. Run past the guard and follow the
path through the grass to the castle. Before you reach the castle, turn off
the path to the left and climb up the wall to the left of the guard and the
main entrance. Jump down into the water and swim down the stream until you
reach the end where it's blocked. Jump out and walk towards the sleeping man.
By now, your Weird Egg has hatched, so use the Rooster to wake him up! He'll
talk to you, then run away. Now, push and/or pull the two blocks where he was
sitting and push them both over the edge. Jump across to the door with an
opening with water coming out and crawl in.