Empty the contents of the sticking wooden drawer and remove it from the dresser.
Run your fingers gently along the guides on both sides of the drawer to feel for rough patches and loose splinters.
Pull off any loose pieces of wood before using sandpaper on a flat wood block to smooth out all the rough areas.
Reach inside the dresser and again use a finger to search the slides for rough spots or broken wood.
Sand down any areas that are not smooth and use a damp cloth to remove wood particles and dust.
Wipe the drawer guides with a damp cloth to remove all the wood dust from the surface. Allow all the wood parts to dry completely before moving on.
Rub a candle or bar of soap to coat both the wooden drawer guides and slides. This will lubricate the slide action and seal out moisture that may cause future damage.
Slide the wooden drawer back into the slides and pull it back and forth to gauge the improvement.