Remove your seat from the seat base that is bolted to (or part of) the floor of the RV. You will typically need a socket wrench to do the job. Once you've removed the seat, place it to the side for safe keeping.
Place the bottom portion of the swivel seat plate onto the seat base in your RV.
Bolt the top portion of the swivel seat plate on top of the bottom portion. Your new swivel plate set should come with the appropriate hardware for this.
Place the seat on top of the new swivel seat plate, and use the accompanying hardware to bolt the seat to the top swivel plate. Once everything is tightly bolted, use the swivel plate's handle to allow the seat to swivel.