How to unlock the riddle quest:
You must succesfully achieve 10 triforce medalions in Four Swords. After that go to the lumberjacks' house and talk to the guy inside. He will give you a box and your first riddle.
How to obtain the Hurricane Blade Technique:
Succesfully complete the riddle quest in Link to the Past. After the last riddle the guy will teach you the hurricane blade techinique. Be careful as performing the technique takes a toll from your magic meter.
How to unlock the "Palace of the Four Sword" Dungeon:
You must beat Vaati's Palace on Four Swords then succesfully defeat Ganon in Link to the Past. After that go to the remaining hole in the Pyrimad of Power and bomb it. This is the hardest dungeon in the game. I recomend that you carry some faries and cure-all potions.
At the place where you get the flippers, go to the first waterfall there is a seceret door. Go in it, there you will find a magic pond. Throw your shield into it, the fairy will give it back but it will be upgraded.
(supplied by: naruto)
In the dark world go to level 4 and upgrade your sword before you go to level 3, this will make this level a lot easier.
(supplied by: vampirechick2000)