Measure the length of your bed, and the height of the gap between the floor and underside of the frame.
Decide on the size of the drawers you want, based on the measurements from step one. In most cases, you'll have room for more than one drawer. Don't make any individual drawer more than 3 feet wide, or more than 2 feet deep. Larger drawers can become too heavy to move easily once loaded. Remember to account for the height of the wheels when deciding how tall to make your drawers.
Cut your lumber to match the specifications of your drawer. You'll need two sheets of 1/2-inch plywood cut to match the height and width of the drawer. You'll need two more cut to match the height and depth. Finally, you'll need one sheet of 1/4-inch plywood cut to match the depth and width.
Sand all surfaces of all your lumber pieces. If you want to paint or stain your lumber, do so after sanding and wait until completely dry before continuing with this project.
Set one width-cut and one length-cut piece of plywood together in an L-shape, held together with a line of wood glue. Use clamps to hold them in place, the reinforce with a line of brads, one for every 3 inches of seam.
Repeat step one with the other width-cut and length-cut sheets of plywood. Wait for all glue to dry.
Arrange the two L-shapes into a rectangular frame, forming the box of your drawer. Glue, clamp and brad the two open corners just as you did with the Ls.
Set the 1/4-inch sheet over the frame you've built, with its edges aligned with the outside edge of the frame. Affix in place with a line of wood glue and then reinforce with brads at each corner and one brad for every two inches along the sides. Wait for all glue to dry.
Attach one wheel mechanism at each corner using your power drill and the accompanying wood screws.
Attach the drawer pull mechanism to the front of your drawer using your power drill and accompanying wood screws.