Visually inspect the piece of furniture. Make sure the item is not leaning to one side, which may cause drawers to stick due to the shifting of the furniture weight. Check drawer railings to verify that none are bent, which could also cause drawers to stick.
Open one drawer completely. Use caution when getting the drawer open fully, and do not force the drawer out any farther than you can achieve by tugging on the drawer. Rub a bar of soap on the drawer track on both sides. Make sure all tracks have been coated with soap. Close and open the drawer a few times to determine whether the soap helped fix the sticking problem. Using furniture wax is an alternative fix for sticking drawers; it works in the same manner as soap.
Check the humidity levels in the room the drawer is located in. Antique drawers will stick in hot and humid conditions. Place a dehumidifier in the room where the drawers are located to help prevent sticking or to solve the sticking problem.