Some people believe that disassembling a roll top desk to make repairs to the tambour is like finding the key to a Chinese Puzzle Box. With a bit of thought, you will realise that, although the makers of roll top desks delight in making their desks a little complicated, they still must be simple enough to assemble and disassemble that furniture repairmen far from the maker can replace parts and panels as required.
Open the rolling top, and unscrew the straps on the back of the desk that hold the top section. You may have to open a drawer to remove screws that come from underneath to hold the top section as well.
Remove the tambour. The tambour is the slatted wooden curtain that slides upward to expose the interior of the desk and slides up from a well inside of, or even behind, the modesty panel of the desk. Remove the tambour's handle if it fits inside the top instead of a well in the lower section of the desk.
Ensure that you have the loose slats properly aligned when you apply the new backing. Turn the tambour over so that the wooden slats are on the bottom, and the canvas is on top. Push one side of the tambour against a straight edge to make sure the slats of the tambour are properly aligned.
Inspect the canvas backing that gives the tambour its flexibility. If it is in bad repair, do not remove it; it still holds the slats of the tambour in place. Use fabric glue, applied with a paint brush, to glue a new piece of canvas to the old canvas. Take care to glue the new canvas not only to the canvas, but to the wooden slats where the canvas has separated from them. Do not lap the canvas past the ends of the slats--which should be bare wood so that they move properly in their guide channels on the top section.
Replace wood panelling in the top or bottom section if required, and replace broken or missing slats in the tambour. Refinish or repaint the desk as needed..