Sounds like you want to install "wainscotting" on your walls.
The easiest way is to install a new baseboard with a dado milled in the top. The dado goes against the drywall. Then you install tongue and groove boards vertically, with the bottom of the boards set in the dado in the top of the baseboard. You nail through the tongue (like installing hardwood flooring) so the nailheads are not visible in the finished prooduct.
You cap the wainscot with a top rail that, llke the baseboard, has a milled dado, this time on the bottoom. Essntially, the dados capture the top and bottom ends of the vertical t&g beadboard pieces.
Wood does move, so it's best to prime and paint (or stain) the beadboard pieces before you install them.
I'm pretty sure all of the pieces (base, verticals, and cap) are available at home centers.