How to secure plywood wall panels with hidden fixings
If you use 3/4" plywood and not a veneered MDF you could drill a small pilot hole for trim head screws. 



It will leave a hole about 3/16" in diameter that will need to be filled after the panels are stained/sealed. That is the best simple way to do it. Even simpler would be to use finish nails. They would leave a hole to fill of about 1/8". The lengths of thew screws or nails are entirely dependent on the material you are going through.

The joints between the panels could be done like a T&amp;G arrangement but will cost plenty over a simple "floating tongue" or spline joint. This will control the movement between panel joints that do not fall on a stud or other suitable backing.



Another way is going the "european hanger" way. It has no visible fasteners, but takes up space behind the panel. As much as 3/4" to as little as 3/8", maybe 1/4", depending on your budget.