Cut out the top, bottom, back and sides for the box out of plywood. The drawers will be built later.
Mark each side of the box to cut dadoes for the drawers to slide into. Spacing is critical in this step. The dadoes need to be cut in the same place on each of the two sides. Leave enough space between the dadoes so that your tallest router bit fits into the drawer. Also, allow some room beneath the bottom drawer. The dadoes will not be cut all the way across the board. Make the last mark 1/4" from the back of each side to show where to stop the cut.
Draw a start and stop mark on the router table fence (Image 1) to remind you to lift the board out of the cut 1/4" from the end of the board.
Using the marks as guides, make the cuts in the first board (Image 2). A 3/4" flute bit will cut about 3/16" into the board. Cutting too far into the board will affect the integrity of the plywood.
Cut the drawer fronts and bottoms out of plywood. Also, cut sides and a back if you are making accessory drawers. Remember to cut the sides and back smaller than the size of the drawer bottom so that the drawer will slide into the grooves properly. Sides and drawer backs do not need to be cut for the router bit drawers.
To make a drawer for router bits, first draw a grid on the drawer bottom (Image 1). The shanks of the drill bits will determine the size of the holes. Use a drill press to drill the holes part of the way through the board. Then, use the depth stop (Image 2) to make sure you don't drill through the board. If the holes are drilled all the way through, the shanks will fall through the holes into the drawer below. Finally, attach a drawer front.