Remove the damaged veneer by pushing your razor scraper forward under it, enough to grip a piece of it, then peel it off.
Use the pad sander to sand the parts or parts of the cabinet surface to be covered with veneer, getting it dull and smooth. Wipe up the dust.
Measure the height and width of the first area. Mark out the dimensions on a sheet of veneer with a square and pencil. Add an inch to the measurements all around.
Use your utility knife to cut out the veneer at the marked lines.
Pull off the paper from the back of the veneer piece. Press it onto the cabinet surface, so it overhangs by an inch all around.
Wrap your wood block in a thick dishtowel. Press it over the veneer, pushing it firmly from end to end to squeeze out the air and get it set.
Cut off the excess veneer from around the edges, using the utility knife. Position the knife at a 45-degree angle along the edge to get a clean, beveled cut.
Repeat for each area that you want to cover with veneer.