Pull the drawer out completely, until it stops. When the drawer stops, it means that the latch has taken hold to prevent the drawer from falling out of the bureau or cabinet.
Feel the sides of the drawer with your hands. Most dressers and cabinets have a latch that you can disengage by putting pressure on the latch, located on the side of the drawer. After you have located the latches, apply equal pressure to both latches.
Hold the latches and lift up on the drawer as you slide it out. Do not release pressure on the latches, as this will re-engage the latch, preventing removal of the drawer. Repeat the process for all of the drawers you want to remove.