How do I flood a mine?

As suggested by BlueRaja - To further my comment on StrixVaria's answer:

You should be able to create a deeper pool using source blocks that you place against a temporary vertical surface.

Basically, fill the bottom of your pool with sources by dropping buckets of water. Keep dropping water until the surface is flat, if you can see water flow into a square, then thats where the source needs to go. This will give an even 1 deep pool. You're not finished yet.

B is solid blocks.

W is water sources.

    B      B
    B      B
    BWWWWWWB
    BBBBBBBB

Build a line of blocks directly over the water sources, this will give you a surface to drop a line of water sources against.

N is the line of new blocks (from the side).

    B      B
    B  N   B
    BWWWWWWB
    BBBBBBBB

Start dropping another layer of water sources in the "trench", using the sides of the pool and the sides of the line of blocks to drop the sources against.

    B      B
    BWWB   B
    BWWWWWWB
    BBBBBBBB

Create a new line of blocks just outside of the existing one, then remove the existing line.

    B      B    B      B
    BWWBN  B -> BWW N  B
    BWWWWWWB    BWWWWWWB
    BBBBBBBB    BBBBBBBB

Drop another line of sources against the inside of the new line of blocks.

    B      B
    BWWWB  B
    BWWWWWWB
    BBBBBBBB

Continue across the surface of the pool until you've filled in the second level. A third level can be placed in the same way.

   BWWN   B
   BWWWWWWB
   BWWWWWWB
   BBBBBBBB

Note that it's possible to simply ignore the lower levels and just have an area of sources on the surface, like this:

   BWWN   B     BWWWWWWB
   B      B  >  B      B 
   B      B     B      B
   BBBBBBBB     BBBBBBBB

This can still be used to provide a pool deep enough to fall into, and which can be removed more easily than a solid pool of sources.

Water physics in minecraft is nothing like what you would expect from true dynamic water physics.

Water has source blocks and other blocks. Source blocks can be picked up in a bucket and placed elsewhere, whereas other blocks simply run off existing source blocks and cannot be collected. Water runs up to 7 blocks away from a source block on flat ground, and can go further if there is a slope. You can read more about water physics at the minecraft wiki.

To answer your question on how to make water deeper, you have to manually collect source blocks and place them at the height you want the water. I have never quite been able to get a customized lake more than 1 level deep to work, but I know if you are patient enough you can place enough water blocks to manage it.

Water in a bucket will take a long time so just keep mining till you reach water.

Or you can mine underground near the sea and once you are certain you are under mine up and woosh! all the water comes down and floods your mine.

If it hasn't gone high enough use water blocks (or source blocks) which will definitely do the job.