Plan Ahead
Draw a scale model of your plans on paper before buying any materials. With detailed plans and finalized dimensions worked on in advance, you will know exactly how much material to buy and you will be much less likely to make mistakes during construction.
Make the Boxes
Ty made the boxes with two open sides, but you will probably be happiest leaving only one side open for use as storage. In most cases, the footprint of the boxes should be 2 feet square, but the height can vary from about 2 to 3 feet, depending on the finished height you are after. For each box, cut a top, a bottom, and three sides. Fasten the boxes together using drywall screws, and sand any rough edges that remain.
Make the Countertop
The safest way to layout the countertop is to set the three boxes in their intended home on the floor, and then set a sheet of MDF on top, with plenty of overlap all around. From below, use a pencil to trace the rough outline of the countertop you want, allowing the top to overhang the boxes by no less than four inches at any single spot.
Flip the MDF over and place it on a couple of sawhorses. If necessary, fine-tune the outline and then cut the MDF with a jigsaw. Have a helper nearby to catch pieces of MDF as they fall away from the countertop. Sand the edges so that they are nicely shaped and very smooth.
Prime and Paint
Take the finished boxes and countertop to the garage or outside or wherever you like to prime and paint them. I suggest one coat of primer, followed by a light sanding, and then two coats of good quality latex paint. When the paint has dried thoroughly, take all of the pieces back to the room in which they will be assembled.