I am working on an acrylic-painted game board and am starting to put polyurethane on it to get a high gloss finish. But being that it is a game board, I think it needs to be put on one layer at a time so as to avoid any kind of marks from setting wet poly on a stand, which leads to my question: what is the proper method of putting polyurethane on the board one side at a time? Would I be better off completely finishing the top, and then start on the bottom? Or should I do the top, let it dry, then the bottom, for each coat?
Top, then bottom, then top, then bottom will greatly reduce the odds of the board warping due to differential moisture uptake/release when one surface is sealed and the other is open to the air. While the acrylic paint is sealing it somewhat, the conventional wisdom of long experience is to try and keep the number of coats per side the same to prevent (or at least reduce) warpage.
Doesn't make any difference, really; the question is number of coats per surface, not order they're applied in.
The thing to watch out for is that there will be a tendency for drips to run down the edges and onto the other face. You may want to use masking tape or other techniques to guard against that, though going with multiple thin coats rather than fewer thick coats will also help (and is the better practice in any case).
(This is one advantage of HVLP spray—the atomized finish dries almost on contact, so it doesn't tend to run unless you seriously over-apply it.)
Always start with your bottom or "B" side. Most things have a side that is unseen or at least less visible. Often these B sides need to be sealed but not completely finished out, so you can apply your sealer coat to the bottom, let dry, flip it, and then finish out your top with out ever having to set your piece A side down with green finish on it. If you put a coat on your show side, then turn it over, if it hasn't completely cured it could stick and ruin the finish. If you have a piece that has no B side, I still prefer finishing one side at a time (time permitting) but if you must flip use these
They'll minimize sticking.