Insert a butter knife in the crack between the top of the dresser and the drawer and try to loosen any obstructive content. If this task proves difficult, your drawer is overfilled. If not, continue to step two.
Remove the drawer and identify any loose nail heads. Hammer these to just below the drawer's surface. If the drawer has runners, rub a lubricant along them. Furniture wax will give you a lasting finish, but paraffin wax, candle wax or even soap will do in a pinch.
Use a hammer to gently tap a small block of wood against the outer, bottom side of the drawer and remove nails with a claw hammer or pliers to see if the bottom of the drawer is damaged or sagging.
Remove the bottom from the back of the drawer. If it only sags slightly, turn it over, slide it back into the dresser, and reattach it with box nails positioned a couple of inches apart. If the bottom piece is cracked, try repairing it by pressing the crack together and gluing a canvass strip over the crack before reinstalling the piece.
Reinforce a worn runner by applying several thumbtacks to the worn spot.