When retrofitting wainscot, tall or middle high on an exiting drywalled wall, we cut horizontal bands through the drywall and install rips of 1/2" plywood at 24" on center. Each vertical board is then glued and nailed to the plywood strips to secure it to the wall. A few things to bear in mind. First, all your electrical boxes will need to be extended to the face of the new panels to provide a fire resistive contact. Second, removing casings and adding jamb extensions to windows and doors will allow the casing to sit "proud" of the new paneling and cover the transition gap where paneling hits door or window. This also gives the baseboard a spot to land. Use care on the hinge side of the doors as with 3/4" material and casing on top, hinge bind is an issue.