Aside from the first and last levels of the dungeon, every pair of floors has the exact same base layout. You'll always want to head four squares south and two hallways west on odd levels, or four squares north and two hallways east on even levels. It's not always that simple, of course, but that's the goal. It pays to map out at least one dungeon for use when questing.
The first time you descend to this level, it will likely be to find a
Gelatinous Cube. As with all
Quests, you are hunting the most powerful
Creature on the floor. In addition to its extreme damage, the
Gelatinous Cube destroys your
Armour when it hits you. For this reason, you may want to go unarmored on
Dungeon Levels 3 and 4. Everything here deals at least 28 damage, and that damage tends to add up quickly. Don't try dungeon delving without sufficient HP.