Pry up the old cabinet floor using a flat pry bar. Start on the front edge and work your way toward the back of the floor until the entire piece of wood is removed. If the floor was fastened with screws, use an electric drill with a driver bit installed to back out the screws. Remove the floor carefully so that you can use it as a template for the new floor.
Lay the old floor on top of a piece of 1/4-inch plywood. Trace the outline of the old floor using a pencil. Ensure that the cutouts for the plumbing are in the same location on the new floor as they were on the old floor.
Cut the piece of plywood along the traced lines you drew using a circular saw. Use a jigsaw to cut out the parts for the plumbing.
Lay the new floor in the cabinet and fasten it to the frame of the cabinet using 3/4-inch drywall screws. Insert the screws using an electric drill with a driver bit installed. Use 3 to 4 screws per side.