Turn the countertop upside down. Turn the sink upside down and center it on the bottom of the bathroom vanity's countertop. Mark an outline around the sink using a pencil. Use a measuring tape to enlarge the outline by 1/8 inch. Mark the faucet holes and predrill them with a 1-inch hole saw.
Use the hole saw to drill a hole inside the sink outline at each corner. These holes will act as pilot holes for the jigsaw. Use a jigsaw to cut along the outline and remove the countertop. Sand around the opening with sandpaper or a file to smooth out rough edges.
Drill holes with a 1/4-inch drill bit around the edges of the sink rim. Space the holes evenly, paying special attention to the corners and midsection between. You want the sink to secure tightly to the bottom of the vanity countertop.
Clean the bottom of the countertop and the top of the flush mount sink with denatured alcohol. Denatured alcohol prepares surfaces for silicone caulking. Without the proper cleaning, the silicone may not form an adequate seal.
Apply a bead of silicone to the rim of the sink. Apply a second bead of caulk to the bottom of the countertop. Place the sink down on the countertop being careful to align the edges perfectly.
Place screws in the predrilled holes of the sink rim. Tighten the screws and any other mounting hardware to fix the sink to the countertop. Clean off excess silicone. Let the assembly dry overnight.
Turn the countertop right side up and install it over the bathroom vanity. Install the sink faucet and drains. Install the countertop using the manufacturer's instructions.