Pull the drawer out of the dresser unit. If it is stuck fast, move the piece of furniture near a safe source of heat and let it sit for a few days. Try to remove the drawer again after the warmer temperature reduces swelling.
Check the drawer to see if there are any protruding nails or broken pieces of wood that is causing the problem. Look into the dresser opening to see if anything has fallen into the area that can keep the drawer from moving properly. Remove any obstructions. Use a hammer to pull any nail that is protruding from the wood and replace it with a new one. Reinforce any metal parts and rub or spray lubricant on the pieces. If a metal part is bent, rusted or broken replace it with a new one.
Rub beeswax, a white candle or a bar of plain soap along the bottom and bottom sides of the drawer. Lubricate any areas of the dresser interior that the drawer will glide over.
Check the bottom of the drawer for any uneven areas if it is still sticking. Sand any uneven portions of wood that is keeping the drawer from moving smoothly.
Re-apply the soap or beeswax lubricant and insert the drawer into the dresser.