Clean the drawer, its runner and the inside of the roll-top desk to remove any sand or dirt that may be preventing the drawer from working correctly.
Rub a thin coat of beeswax, soap or candle wax on the rails of the wooden roll-top desk drawers to reduce friction. Silicone-based or other types of lubricant can also work. Use a lubricant safe for wood.
Tighten any loose screws in the construction of the drawer box, using a screwdriver. If the hole is stripped, use a larger screw. Replace any loose nails with screws of a larger diameter.
Plane or sand the warped wood on the sides or bottom of a drawer if the warp has caused the drawer to stick in the roll top desk.
Replace any missing or broken hardware on the runners inside the roll-top desk. Clean bearings with ammonia and reapply lubricant.
Rebuild the drawer itself in extreme cases where the wood has deteriorated and split beyond repair.