Despite "Dragon" is Level 6, this labyrinth should be visited after Demon.  Dragon is a very difficult labyrinth but preparation is very difficult.

First of all, if you haven't gotten the Bow and Arrow, do so now.  The Bow is found in Level 1; the arrow can be purchased in certain stores in the overworld.

Second, get a full set of bombs and make sure that Link has the Magic Shield.  The Magic Shield is very critical in Dragon since the Wizzrobe's spells cannot be blocked without it.  The Red Candle is more effective than the Blue as it can be used several times in the same room, not just once.

Now stake off to the graveyard.  Just east of the graveyard is a passageway that takes you into Dragon.  Don't go up that passageway yet.  Instead, continue east one scene and plant a bomb in the mountain in between two passageways.  A secret door should open if you do this correctly.  There, you can get medicine -- which is very valuable in Dragon.

Now return to the passageway that is one scene east of the graveyard.  Now go north in that passageway and into Dragon we go.