Pull the Thomasville dresser drawer out as far as it will go. The drawer will usually stop short of opening all the way, to prevent it from falling out of the dresser.
Feel along the sides of the Thomasville dresser drawer. There should be a small button, located along the bottom side of each drawer, that will allow the draw to come free from the guide. Press the button.
Lift up on the drawer while pressing the button to remove it from the dresser.
To replace the drawer, hold down on the button and place the drawer back on the guides.