Pull the drawer out from under the bed and empty it of all contents.
Examine the bottom of the drawer. Most will be made with the bottom panel run through a slit in the side -- and possibly the back and front panels. Others attach the panel with finishing nails or wood screws.
Remove the back of the drawer. If attached with screws, remove it by loosening the screws. If attached with glue, gently tap it loose with a hammer. Use a washcloth or similar pad to protect the wood while tapping.
Reset the bottom of the drawer by setting it back into its original position. If it runs through a slit, run a thin line of wood glue in the slit before inserting. If it attaches via screws or nails, run the glue along the edge of the panel.
Reinforce the connection by driving finishing nails through the side panels of the drawer into the edge of the drawer's bottom. If the panel is more than 1/4-inch thick, you can use wood screws instead for an even stronger structure.
Set the back panel of the drawer back in position. Hammer or screw into place as appropriate.