We have a dry basement with a concrete floor. When putting on the wall boards, how much (if any) gap should there be between the concrete floor and the bottom of the board? The boards are 3/8 inch, I was thinking about using a scrap piece drywall on the ground and then resting the board on top of it while installing, and then pulling it out when finished.
Drywall should definitely not touch concrete as moisture will wick (ie flow up the surface as in a candle/lamp wick) into the drywall and encourage mold growth.
3/8" should be sufficient - your prop up plan is not only appropriate, but a common technique used by drywallers.
1/2" give or take is fine, just be sure there's no direct contact that can wick up moisture. The trim will cover any gaps, so it's not critical that these are even.
Note that drywall on the wall should support the ceiling drywall, meaning you install the ceiling first, and the wall is installed tight against the ceiling. For the bottom piece, you use a roll lifter under the drywall to lift it up and give you a tight fit to the board above it. You rest the drywall on the small lip on the end of this lifter and then step on the other side as a lever to raise it up.
If using 3/8 drywall , you should first run a strip of 3/8 plywood along the floor first.
The height will be determined on trim height.
This will do 2 things,
First , it will act as a moisture deterant ...easier to replace a 2 - 4 " piece of plywood then a whole sheet of drywall.
Second, it will allow you to install the trim much easier and faster! you won't have to worry about hitting a stud for each trim nail.