Pull out the drawer as far as it will go and empty it of all its contents.
Hold the drawer in your hands and pull it up and out. In some cases this is all you need to do to remove the drawer.
Look for a tab or button that may be holding the drawer in place. Press the tab or button and pull out the drawer to remove it.
Look for a screw that's holding the drawer to the chest. Unscrew it from the chest with the screwdriver and pull the drawer out to remove it.