Cut a piece of wood (at least a half inch thick) to 8 inches to ensure it fits the height of a normal DVD storage case. The piece should be 1/2 inch long for each case -- 10 inches if you're storing up to 20 DVDs.
Measure two wood pieces to the same length as your first piece and 7 inches wide to ensure it holds the width of a DVD case. These pieces will make up the top and bottom of your console.
Paint or stain these pieces as you see fit, applying the paint/stain across all sides and edges with a brush, and wait for the stain or paint to dry. This will give the wood a smooth finish and protect the cases you are storing.
Lay the 8-inch piece on a table and glue the two 7-inch pieces to its sides with wood glue, butting up the 7-inch pieces against the edges of the 8-inch. Wait for the glue to dry.
Measure two more pieces of wood to the height and width of your currently assembled console -- it should be 7 by 9 inches square -- using the console itself as a stencil. Trace the wood along one of the console's "open" sides.
Cut out your traced side pieces, paint/stain them as needed and glue them to the open outer sides of the console.
Drive nails into the ends of the console where the wood pieces meet using a hammer if you want to make the console more sturdy.