Saw out the wood panels to the size box you want. Place the wood on the table saw and cut to your measurements. For example, cut the panel for the bottom at 12 1/8 inches by 26 inches long, the side panels at 12 1/8 inches by 10 3/4 inches high. Saw the front and back panels at 11 1/2 inches by 26 inches.
Fit the panels together without gluing or nailing. Ensure that the measurements match the size box you want. Place the bottom panel on the floor and match the sides, front and back to the bottom piece of wood. Saw the panels if necessary until the box measurements are right.
Attach the front and side panels with glue. Screw in the wood screws with the drill. Glue and screw the back panel until you have the frame together. Affix the frame to the bottom panel with glue and screws.
Cut out the lid to match the box's dimensions. Place on the hinges about 2 inches from each side of the lid. Drill in the hinge screws until secure.
Sand the box with sandpaper until smooth. Wipe off the sawdust from the box before staining. Apply the stain according to the manufacturer's instructions. Smear on the stain in a small area. Wipe off the excess for an even coating.
Allow the stain to dry. Attach wheels to the box at the four bottom corners by drilling in he caster screws.