Step 1: The problem
Step 2: Remove the crud
Note that the surface below this is, on my desktop, just plywood. Well, this whole thing works just great even if you didn't build your desk yourself from scrap iron and use cheap plywood for a top...
Step 3: Removed the damage
Again, this all tore the way it did because I use wood glue on plywood. I do this because this is the primary surface of my bench and I don't care - but believe me, it works just as well using white glue on nicer tops. If you have a formica countertop, white glue with this stuff works great and it wont tear as easily. Mine usually doesn't even tear this badly, but I put off replacing it longer than usual and it was pretty badly cut up.
White glue also cleans up easily with warm water, so the next step wont be needed if you are starting with a nicer subsurface.
Step 4: Clean up a little
Old formica surfaces, on the other hand...
Step 5: All cleaned up, the magic begins
Note that you don't need a GREAT surface to start with. My desk uses a piece of old exterior grade plywood I happened to have lying around the day my dad and I welded it up, and it works great. With the neoprene top you can't feel an unevenness and it looks great. And no slivers!