Recently remodeled bathroom. Time to install vanity and top. New coutertop with undermount sink has separate side & backsplash. My question... how do I install the backsplash to the back of the countertop, glue, adhesive? Thanks in advance.

What material is your counter top? Corian and granite back and side splashes are usually just held in place with a bead of silicone on the seam and a few globs on the back, press up againist the wall.

Granite

Yep, just glue it to the wall with the same silicone you seal the seams with. I generally use clear silicone and it does seem to disappear.