Remove all of the trim and base molding around the perimeter of the carpet. Unscrew or pry off the trim under the cabinets as well.
Cut around the perimeter of the carpet with a utility knife. Pull the original carpet and pad off the floor of the RV. Discard the old carpet and pad. Remove exposed nails and tacks with a pair of pliers. Scrape old adhesive from the floor with a metal scraper.
Put adhesive tape or carpet adhesive along the entire perimeter of the room. Use the same adhesive to draw six foot by six foot X's across the floor of the RV.
Roll out the carpet pad in the RV. Allow three inches of overlap around the perimeter of the space. Trim the pad with a utility knife around the walls and cabinets.
Put adhesive tape and carpet adhesive on top of the carpet pad in the same pattern you applied the adhesive to the floor of the RV.
Roll out the carpet, leaving three inches of overlap around the edges. Trim the carpet with a utility knife to fit snugly inside the walls of the RV.
Move the carpet roller over the carpet to press it firmly into the floor of the RV. Step around the edges where the roller won't reach. Trim any loose threads with the utility knife.
Reinstall the baseboards and trim molding around the perimeter of the room.