Use a utility knife to slice through the caulking between the countertop and the wall. Score along the seal between the countertop and the cabinet.
Lift the countertop off the cabinet to break the seal, and periodically use a pry bar to help break the seal along the wall.
Many countertops are screwed into the vanity; if this is the case, be sure to remove all of the screws before trying to lift off the countertop. Another option is to remove the entire vanity/sink combination; however, you might need an assistant to help you move the vanity.
If the supply lines for the vanity come up through the bottom, there may not be enough clearance to lift the vanity over them. So, first use a small handsaw to cut away some of the bottom of the cabinet around the water supply lines. Then lift the cabinet up and over the supply lines and take it out of the bathroom.
Your removal may differ depending on the location of your water supply lines and the type of cabinet you are removing.
If your supply lines come up through the floor, you might want to consider hiring a professional to relocate them, too. The relocation of supply lines may leave two holes in the floor. Because a pedestal would cover most of the holes, fill them with grout. Plug the holes from underneath the floor, fill them with grout, wipe away the excess grout and allow the grout to dry.
Position the sink and pedestal against the wall, making sure the sink is flat against the wall and correctly seated on the pedestal. Use a felt tip pen to mark the locations for the holes needed to mount the sink and pedestal.
Using a hammer drill with a masonry bit, drill pilot holes into the wall at the marked locations. Begin drilling with a small bit and then change to a larger bit to increase the size of the holes so the supplied toggle bolts and lag screws will fit.
If you aren't drilling through tile or masonry, a standard drill bit will work.
To simplify the installation, assemble the sink and faucet before mounting the sink to the wall. Start by spreading plumber's putty around the faucet hole in the sink. Insert the spout shank of the faucet through the deck of the sink and secure it from underneath.
Spread more plumber's putty around the hole for the faucet handle, inserting the handle and then tightening it with a fastening nut from below. Attach the flexible hoses to the bottom of the handles, tightening them with locking pliers. Be sure to tighten the nuts to secure the connections.
After the faucet assembly is installed, begin working on the drain. Press a roll of plumber's putty to the underside of the drain flange. Insert the drain through the drain hole of the basin. Pull the flange down and seat it in the putty. Insert the rubber gasket and plastic washer, and then hand tightened the mounting nut.
Insert the stopper and assembly, and attach it. Connect the water supply lines to the faucets.
With the sink fully assembled, it's ready to be installed in the bathroom. Position the pedestal over the holes drilled earlier. Carefully lift the sink and place it on top of the pedestal, lining it up with the pre-drilled holes.
Insert the supplied toggle bolts and tighten them with a screwdriver. Insert lag screws to secure the pedestal to the floor.
Join the water supply lines from the faucet to the shutoff valves. Put the P-trap in place and tighten the slip nuts that connect it to the tailpiece and drain arm.
With all the connections made, open the water shutoff valves and turned on the hot and cold water faucets one at a time to slowly bleed off air in the lines. Fill the sink with water, then let it drain to check for any leaks.
Run a bead of silicone caulk between the wall and the sink to seal any gaps against moisture.