What's the easiest or quickest way to build bases under water?

Actually there are some awesome tricks I used to build Atlantis on my server--they all stem from the fact that water cannot occupy the same square as anything else.

First of all bring a door with you. When you are down there, set it on the ground, open it and step in. You will be in an air bubble. This can be done any time to catch your breath and it's not a bad way to escape from monsters at night.

Secondly signs, ladders, fence-posts all resist water and can be used as blockers. I played with all these for a while:

Signs aren't stackable, you spend all day running back and forth building them.

Fence-posts block you so you can't just swim up and down, overall they will work but are unwieldy.

The best solution I found was ladders--but place them ABOVE your head. You can still jump up and down through them, but if they are at your level you will climb up them every time you move--it's really frustrating (This is no longer true in the latest version making ladders the clear winner).

There is a pattern where you have one block above you with ladders on each side, the a "Knights move" to the next block with ladders on each side. It makes a good roof with no more blocks than you need.

If you want the water to be right over your head in some areas, use signs.

The knights move I was referring to is the L shaped move they make in chess. You can make a ceiling of blocks like this:

 . . . . * . . . .
 . * . . . . * . .
 . . . * . . . . *
 * . . . . * . . .
 . . * . . . . * .
 . . . . * . . . .

Where the "*" are blocks and the "." are empty space. Note that in this pattern, each "." is adjacent to a * (and therefore are actually filled with a ladder attached to the *).

What I do is to build a walkway over the water and use it to drop sand to fill the area I want to be air. I then build the walls and ceiling around the sand before digging out the sand from below. Afterwards remove the walkway if you want to and you're done.

You can also use sugar cane to breathe under water. Note, that you need to place the sugar cane next to a "hole" with water.

So i usually dig two blocks, fill one up with dirt, and place two sugar cane's on top of the dirt. Now you can stand inside the sugar cane blocks and take a breath ;)

Btw, if you dig, shovel, etc. while standing inside the sugar cane blocks, you're working as fast, as if you were standing on land ...