Like carpenter said, the screws are just holding the wood together while the glue dries.
In the end, it is the chemical bond between the glue and the wood that is truling holding the two pieces of wood together. If you really wanted to you could take out the screws and the boards would still be pretty **** stuck together.
Every 4-5 inches is optimal and would insure the best seal/bond, but it is really not needed. You could go every 6, maybe even 7 inches and still be fine. Just use a lot of wood glue //content.invisioncic.com/y282845/emoticons/wink.gif.608e3ea05f1a9f98611af0861652f8fb.gif .
Basically the steps are:
1. Measure what you need.
2. Measure again!
3. Cut pieces
4. Clamp or hold two pieces together
5. Predrill screw holes
6. Put lots of wood glue on one piece
7. Stick two pieces back together and clamp
8. Screw
9. Repeat until box is done, but before you put the top of the box on, seal all the seams with silicone to insure an airtight seal
Trust me, it sounds bad at first. And when you first are about to begin you will be a little hesitant. But after you get started, you realize it really isn't that bad.
Good luck on the build!