Collect old drawers. Find them at flea markets and thrift stores, in your attic or your mother's, or at curbside on trash day. Look for random sizes and character. Knobs and drawer pulls are a bonus. Haul your finds home, and wash them down with a vinegar-and-water mix or mild soap, then dry them off.
Sand any rough edges to smooth splinters. Remove knobs to paint separately. Arrange the drawers flat on the floor in various configurations to see what looks good. Try to keep the deepest drawers on the bottom of the wall, unit but vary the shapes and sizes. Your final design should seem balanced but not "neat." Make a sketch of what goes where, and put numbered stickers on the drawers to keep track of them.
Place each drawer on a drop cloth and paint, decoupage, stain or otherwise embellish it. This is the time for creative genius. Be as ornate or as simple as you like. Use primary colors, black and white, wood stain, chintz or cartoon print fabric; anything goes. You can paint or gild the various knobs. Include your child's brilliant crayon depiction of a fire engine carefully decoupaged inside a drawer so it seems framed.
Clear coat special artwork with lacquer when you are through, but don't bother lacquering the entire assemblage. Screw the knobs back on drawers that are on the outer edges of the wall unit design.
Reassemble the design according to your sketch, and connect the backs of the drawers with metal braces. Set a brace on the joint of two drawers, mark holes for screws in pencil, tap a shallow starter hole with a hammer, and nail and then screw the braces to the wood.
Stand the wall unit up, place it against the wall, and mark the four places at top and bottom corners for wall braces. Screw the braces to the unit, mark the spots for the wall screws in pencil, drill holes in the wall for the screws, and attach the braces to the wall to secure the unit.