for all the drawers except the bottom one:
pull open the drawer directly under the one you want to remove all the way.
pull the drawer open that you want to remove. there is a screw on the outside at the front of the inside part of the slide. unscrew it, and keep track of it. once you have done this to both sides, life up the front of the drawer about an inch, and then pull it away from the box. the drawer will drop down onto the drawer you opened below it.
when you get to the bottom drawer, put something (a box or step stool) under the drawer after you open it. it is held in by 4 screws on each side. undo the first three, starting from the front of the drawer. this will cause the drawer to sag onto whatever you put below it. carefully remove the remaining screw on each side. keep track of the screws.
did i mention keeping track of the screws? they are pesky little buggers, and seem to get lost easily. the drawers are tapped for them, and they seem to be made of unobtanium, since i have never found a replacement of the correct size and length.