Shut off the water in the piping by turning the valves under the sink.
Loosen the connector at the top of the P-trap with a wrench. The P-trap is the curved pipe attachment that connects under the sink. Remove the P-trap once the connector is loosened.
Insert the tip of your putty knife in the seam where the vanity cabinet meets the wall. Start at the bottom and work your way up, loosening the caulk as you go. Repeat on the other side of the vanity cabinet.
Insert the tip of your putty knife in the seam where the vanity counter meets the cabinet. Work your way around the sides of the counter until it can be popped off the cabinet.
Remove all screws on the inside of the cabinet that hold the cabinet to the wall with a cordless screwdriver.
Remove the vanity from the wall. Fit a new vanity in the old one's place.
Locate the studs on the wall and mark them. Secure the vanity cabinet screws to the marked areas on the wall.
Fit the vanity countertop and sink over the cabinet. Attach the P-trap to the piping on the bottom of the sink, as well as the water pipe in the wall.
Line caulk along the seams of the vanity with a caulking gun and let dry.