Remove the items you mounted with the double-sided foam tape as carefully as possible. Disengage one end of the frame, light shelf or other item, then carefully pull that item away from the wall while holding the tape. Removing items carefully can reduce the amount of double-stick tape left behind.
Place a razor blade in a holder and carefully lift one end of the double-stick foam tape. Peel the tape away from the wall carefully and remove as much of it as possible.
Soak a sponge or soft cloth with a commercial adhesive remover. Use just enough to make the sponge or cloth wet, then hold it against the wall to soak the foam tape.
Slide the razor blade under the foam double-stick tape and lift up carefully. Peel the tape away slowly. If the remaining tape is still sticking, reapply the solvent to loosen the adhesive on the back.
Plug a hair dryer in to the nearest electrical outlet. Turn the dryer on to the highest setting, then apply the heat to the walls to loosen the double-stick tape. Carefully scrape the residue away with a razor blade or putty knife.