Pry the tops off the two plastic hinges in back of the seat with a screwdriver to reveal the screws underneath.
Secure the nuts underneath the toilet one at a time, then use a screwdriver to unfasten the screws from the top of the toilet. If the nuts are really tight, use a pair of channel locks to keep the nuts in place while the screws are turned.
Lift off the old toilet seat and remove the old adhesive patches around the holes. If necessary, employ a putty knife to remove the adhesive patches. Use mineral spirits on an old rag to insure the area is completely clean.
Remove the backing off the square pads that came with the new seat and stick the pads over the holes on the toilet.
Place the toilet seat so the hinges are positioned over the holes on the toilet.
Secure the nuts one at a time under the toilet. Insert each screw through a hole in the top of the toilet and through a hinge, then tighten with a screwdriver. Snap the tops of the hinges into place so they cover the screws.