I wouldn't glue it on to plywood with mortar.

E-how has a number of articles on DIY projects. My guess is that the proper technique will include a moisture barrier stapled over the substrate, with mesh applied to this with fasteners, with the mortar & stone applied to the mesh. Happy Houzzing.

you could glue them on with silicone I have seen a few hacks do that, but the stone might jiggle a little bit every time you walk by.
otherwise like DMH said.

So maybe the best bet would be to cover plywood with cement board then?

Look on youtube for videos related to putting stone on a wall, and see what the pros recommend. It's amazing the number of how-to videos on doing just about everything you can imagine. Watch a few to get the different takes as different people do things differently, but look for the consensus of the best way to do it.