Move a stud finder across the wall above the vanity to locate all of the studs in the area where the mirror will be mounted.
Measure the width of the mirror. Cut J-molding the width of the mirror using a hacksaw.
Drill through the back edge of the J-molding at the stud locations. Drill a hole for each stud within the width size of the mirror.
Position the J-molding level against the top of the vanity or backsplash. Screw through the hole into the stud at each hole along the length of the molding.
Place the mirror face side down. Install a tube of mirror adhesive into a caulking gun. Squirt half-dollar-sized globs of adhesive 6 inches from the top left edge. Space your next glob 12 inches to the right. Continue adding adhesive globs until you reach the right side. Add more globs below the top row every 12 inches until you reach the bottom.
Turn the mirror to face you, and lift the mirror into the J-molding along the bottom edge. Center the mirror on the molding and tip the mirror to the wall. Press the mirror firmly with your fingers to spread the adhesive onto the wall.
Add mirror clips every 18 inches along the top and each side of the mirror. Insert wall anchors into the walls. Position the clip over the edge of the mirror, and screw the screw into the wall anchor. Secure all sides of the mirror.