Wipe down the top of the vanity around the drain cutout with a damp cloth. Remove any dust or debris that could upset the seating of the sink. Wipe down the bottom of the sink as well, and let both areas dry.
Test the fit of the vessel on the counter. Line up the drain holes of the vanity top and the vessel and straighten the sink out so it lays evenly. If the sink is rectangular and square, check to make sure the front of the sink is parallel to the front of the vanity top. Make a mark on the vanity top in grease pencil where the sink will be installed so you can find this placement again.
Remove the sink from the vanity top and set it aside. Squeeze a line of silicone caulk adhesive around the drain cutout, and a second line near the perimeter of where the sink will be located. Lift the sink up above the vanity and line it up with the grease pencil mark. Carefully lower the sink into place.
Drop the tail piece of the drain through the two drain holes and use a pipe wrench to connect the tail with the P-trap of the drain extending out from the wall.
Wipe away the grease pencil mark with a damp cloth.