Sand each surface to be covered with veneer, using a vibrating sander. Sand it just enough to get the surface dull and clean. Wipe off the dust.
Measure the dimensions of the first span. Transfer the dimensions to a sheet of wood veneer, using a square and pencil. Add an inch all around.
Use a razor knife to cut out the piece at the marked lines.
Peel off the wax paper that's on the back of the piece. Press it to the surface, letting it overhang by an inch all around.
Wrap a dishtowel around a 2-by-4 wood block and press it over the veneer, starting at one end and working across to the other to squeeze out any air and get it firmly set.
Cut away the excess veneer from the edges, along the corners with a razor knife.
Repeat the process for each span.