In order to access the wood desk cover, you'll need to first take the back panel off of the desk. It should be held on with small nails. Once the back is off, you should be able to pull the roll top right out of the track.
After taking it out of the desk, I realized that a roll top is constructed of wood slats attached to a fabric backing. The fabric on mine was old and had worn enough to allow the slats to pull apart. All that you'll need to fix the desk is some heavy duty fabric and glue (I used wood glue, but I'm sure craft glue would work as well).
Cut the fabric to be about four inches less than the width of your roll top and just slightly less than the length.
The roll top on my desk was only broke into two sections, so I did not tear the old fabric off and re-position everything. If yours is broken in many pieces, though, it may be wise to take each section apart and glue it back onto the new fabric piece by piece. Be sure to apply enough glue that all the fabric is attached securely onto the wood.
Allow the glue to dry completely.
Since I was painting my desk, I also wanted to paint this section on both sides. Painting a rolltop is a lot easier if it is done before putting it back in the desk. If you are interested in painting over the fabric to make it "disappear," it helps to thin the paint out a little with some water. Allow the paint to dry and then insert the roll top back into the track.
Once the section is back in the desk, reattach the back panel with nails and your desk is fixed! Isn't that a simple fix?
And be sure to check out the complete post on my desk in case you missed it!