Since no one else has offered up anything, I guess I'll chime in with my 2 cents worth.
It's too late for the first advice I would have offered, which is don't do it. It's way too dang much work to be worth while. Plus, you have to presume that the surface of the plywood underneath it is of the minimum quality...there's no reason to use a good-surfaced plywood if it's going to be covered with rat fur.
But since you're in it now... it all depends on what mastic that the manufacturer used for the carpet. It's not uncommon for a builder to spray an even coat of contact cement for that purpose, in which case, you may really be in for a tussle. I have also seen evidence of builders just putting a few beads of whatever adhesive they are using around the edges and a few more in the middle of larger, uninterrupted panels. But at any rate, I can't offer you much more advice than just scraping away at it with a paint scraper or maybe lifting up a corner and grabbing it with a pair of pliers and ripping away. There doesn't seem to be anything like a magic solvent that will dissolve that old adhesive. At some point, you want to have removed enough of the old covering that you can attack it with something like a belt sander or a large rotary rasp chucked into a drill. You'll need something pretty coarse, like 100 grit sandpaper to remove the remnants of the glue and carpet...BUT, you have to use some finesse, because you can go through the surface veneer really quickly. It would probably be smarter to do this with hand sanding, but I'm too lazy and impatient to do that my own self...it kind of depends on how much surface area you have to do. And of course, once you get all the glue off, you'll have sanding marks from the coarse paper that will require further sanding to smooth them out. And to be honest, what you'll have left won't really be what one would call stain-grade. At that point, I would recommend you look into painting it with Duratex.
Sorry if this sounds discouraging, but I do wish you luck in your endeavor. Keep us posted as to how it goes.