Remove the drawer from the piece. Inspect the drawer for any cracks, loose sides or any damage to the drawer glide on the side of the drawer. Inspect the interior of the piece to ensure the drawer glide is still functional and not completely broken.
Fix any structural problems with the drawer. If the sides of the drawer are loose, tighten the screws or lightly tap them back into place with a hammer. If the drawer is glued, apply some wood glue and press the loose area into the glue. Use a wood vise clamp to hold the pieces together until the glue dries. If you see any rough spots, sand these down with sandpaper. A medium or fine grade will be sufficient.
Fix the drawer glides. If a glide has been broken, it will need to be replaced. Replacement guides can be found at a hardware store. Remove the old glide and insert the new one using a screwdriver. If the glide is simply bent, use a wood chisel to gently pry the guide back into place. You can also use the chisel to remove any built-up dirt that's catching as you slide the drawer back.
Replace any necessary hardware. Antique pieces sometimes have loose or missing hardware. Try to match the existing drawer pulls, but if you can't, you will have to replace all of them. Unscrew the existing pulls and replace them with new ones.
Replace the drawer. Put the drawer back into the piece and slide it back and forth. It should work smoothly.