Remove all the items stored under the sink.
Pry off the old floor using a hammer to wedge a flat pry bar between the floor and the cabinet in the nail locations. Use the pry bar to remove the nails. If possible remove the old floor in a single piece so you can use it as a template for the new floor.
Draw the shape of the floor on a piece of paper and include a rough sketch of plumbing or notches.
Measure the length and width of the floor and locate them on your sketch. Measure the distances where any cutouts for plumbing or notches for the cabinet must be located. Place those on your sketch.
Cut a piece of 1/4-inch plywood the proper width and length using a jigsaw and make the proper cutouts and notches according to your sketch. If the old floor was removed in one piece, simply lay it on top the new wood and trace around it.
Lay the new floor in the cabinet and make any small adjustments that are needed to make it fit. Sometimes all you need is a piece of 80-grit sandpaper. Nail the floor in place using finish nails and a hammer. Place 4 to 6 nails along each side of the floor.
Brush on two to three coats of a water sealant with a paint brush to help protect the floor from moisture.