Vacuum the plywood desktop. Wipe the back side of the furniture-grade plywood sheet with a dry rag.
Fill the paint pan with wood glue. Roll the paint roller through the glue.
Roll an even coat of glue on the desk top and the back side of the furniture-grade plywood. Let them dry to the touch, but not overnight.
Center the furniture-grade plywood on the desk top, glued sides touching.
Heat the iron to "high" or its hottest setting. Lay a piece of brown craft paper at the center of the furniture-grade plywood. Press the iron against the paper, moving it back and forth across the paper in a small area. Heat the wood well, and keep the iron moving.
Move the paper over slightly and iron again, working toward one edge of the desk top. Iron from the center of the plywood out in all directions until the two pieces are fused.
Check for lifted areas where the glues did not bond. Heat them again until they do.
Set a 3/4-inch sheet of plywood or MDF on top of the desk. Place heavy objects on the sheet in several areas to weight it evenly across the piece. Inexpensive bags of garden lime, bricks or any other weighted object will work. Leave the desk to cool overnight.
Remove the weights and the 3/4-inch sheet.
Attach an all-purpose bit to a rotary tool. Trim the top layer flush with the original desk top.
Sand the edge of the desktop by hand with medium-grit sandpaper.
Heat the iron according to the iron-on veneer's instructions. Unroll the veneer strip. Place one end of the strip against the edge of the desk top. Align the top edge of the veneer with the top edge of the desk. Iron the end of the veneer strip to the edge and let it cool until it holds. Iron the veneer strip around the entire desk top edge until you return to the starting point. Cut the end with a utility knife and iron down the seam.
Shave off any excess veneer that projects below the bottom edge of the desk top with a utility knife. Sand the bottom edge by hand with fine-grit sandpaper.