How can I repair water damage under the kitchen sink?
There is a sub-panel between the bottom of the cabinet and the
actual floor. Measure the board so you can create a new one (You can
also get a piece of cardboard to create a template to cut from -
works great with a cabinet with many angles.). To remove it (since
it's particle board) you can just break it out with a hammer. **Be
careful not to damage the spacer board that helps support the middle
of the panel. If you damage it or if it's in bad shape, you'll need
to cut a new piece to replace it. 
When you measure and cut the new board, you will most likely need to
cut it half to get it under the sink. You'll need to figure this out
and make sure to add a quarter inch (width of the saw blade) to the
width of the new board to compensate for the cut in the middle.
Again, you might need to put in a space board in the center for
added support. You'll also need consider where the pipes come in which might be from the floor from the wall. If from the wall, it will of course be easier.
Once the new board is in, you can use the Sintra panels. Or get a
piece of linoleum to cover it so you can help prevent water under
the sink as well as hide the center cut (Or any bad cuts you might
have made in the process). You could also get the 12"x12" adhesive
panels.


Tools


drill,
skill saw or table saw,
possibly a jig-saw
tape measure
safety glasses.


Hardware


screws
maybe nails