The correct way to do this would be to gut the cabinet (remove head, boards, etc.) and replace the bottom using a new piece of plywood. You will need to make sure that the sides are in good enough shape as well.

As for glue, carpenter's glue with the proper clamps, etc.

Not sure if I would attempt this repair with everything assembled.

Each side of the cabinet has a groove near the bottom. The bottom should have a tongue on each side that fits into that grove. It can't sag unless grove or tongue are at least partially missing.

If the tongue is just broken off the bottom you can replace the bottom and be ok. Slide the new bottom into place, glue, clamp, and dry.

If the sides are rotted and the grove broken away there is nothing to hold the bottom in place from below. If that's the case you might try L brackets on the outside of bottom and inside of the sides. Glue into position and clamp until dry.

Hey Rush.
That bottom looks like particle board. if it is warped, you will NOT have any fun tryin to straighten it.
The cabinet prob is too.
Like Gearhead said, gut it, and replace that bottom board with new plywood.
Then, you may want to use a couple L brackets on the inside to help hold in place.
Elmers wood glue, a few headless nails, and some clamps shud do the trick.
If, however, I am completely full of it, then use Pinplayer's technique.
good luck.