Really nice plywood is expensive. FYI - You can get it pre-finished. Check out one of my local sources for ideas.
Look for architectural panels.
Attaching will be with construction adhesive and nails. Depending on the plywood you can go over studs directly or you may need to go over drywall if its thin like paneling.
I saw this done once where the fasteners were incorporated into the design. They used black lag bolts with allen wrench sockets. The panels had finished edges, painted black. The panels were about 2'x3' if I recall correctly. and they had about a 1.5" space between them. They were shimmed down from a main ceiling by about 1.5". The main ceiling, or sub ceiling if you will, was also painted black. The panels were a pre-finished mahogany wood.
It looked really neat. I considered doing this in my basement.
There are also beadboard options, in sheets or boards, that look nice.
Bottom line - This can be a real architectural feature or it can be a red flag when you go to sell, depending on how its done. If you just want to tak up plywood to cover some problem and avoid mudding thing you may be going down the wrong path. If you are doing it for design reasons then go for it and make it nice.
Take pictures as you go.