Probably the easiest and cleanest way would be to make your measurements, and use butt joints for the sides and front and back. Cut the slots for the drawer bottom and assemble the basic box with glue and a few brads. Not the strongest but quick and easy. If you want stronger corner joints you may want to take some time and use half lap joints or finger joints. If you use the butt joints, I would suggest using gussets under the drawer bottom for added strength. Hope this helps.
Making saw dust in Turtle Creek, PA.