DM: "You are in a chamber about 30' across to the south and 30' wide east and west. There are 10' wide passages to the left and right and ahead, each in the center of their respective walls. The stairway you descended likewise enters the chamber in the center of the north wall.
-- Gary Gygax, Dungeon Master's Guide, pg 97.
Why cardinal directions? Why give directions by the compass anyway? "The room has a door to the north, and a corridor branching off it to the east by southeast." What? How do we even know? In GURPS, a character with Absolute Direction will always know which was is north. But otherwise? But in the early D&D stuff I grew up with, of course you knew. All directions are given by compass points or by relative direction and compass point.
Somewhere along the line - probably around when I started to run GURPS - I stopped doing this. I started to get vague. No more "You enter a 30' by 30' room with a 15' ceiling through the arch in the east wall and doors to the north and south" and a lot more "You see a roughly 30' square room with a tall ceiling, and doors to your left and right." Or "it's about a dozen yards in either direction, and the ceiling is about half that high, maybe lower. There is a door in the center of the wall to your left and to your right."
I think this approach has some advantages and disadvantages:
This allows for more natural confusions and getting lost. Always describe it as they see it, not how it relates to the world.
This allows for dungeons that don't orient on the cardinal north. You don't need graph paper or map orientations (unless someone can tell north). It's all relative.
It makes for simpler descriptions, too.
It rewards asking questions and checking the facts in game. Suspect the walls don't quite match up with upstairs? Measure, and maybe there is a secret closet there.
It's harder to confuse people with mis-direction magic or traps that make "south" seem "north" and vice-versa, such as you find in one Basic Set module I'll leave unnamed. Left is just left.
If you get people who obsess over map accuracy, they're going to pace out rooms and measure walls and all of that, and slow down the game when it's not actually useful to do all of this.
You can end up making the same vague statements of size all the time, so the players always know that "About 10'" means 10', or "roughly 10 yards on a side" means 30' x 30'.
For all of that, though, I prefer to give relative directions. It just feels more right to me - gives me more of a feeling of verisimilitude.
How do you give directions?
And how specific are you with sizes?