Measure and cut four 20-inch squares from a sheet of 1/4-inch thick plywood. On the bottom of each square, make marks at two inches in from each side and one at 10 inches in (the center of the board) and five inches up from the bottom.
Draw a line connecting each of the 2-inch marks to the 10-inch mark with a straight edge, forming a triangle at the bottom of each piece. Cut out the triangles with a saw.
Cut four 20-inch lengths of square dowel and one 6-inch length. Lay one of your boards over two dowels. The dowel pieces should be aligned with the board's right and left sides, keeping the cut triangle at the bottom. Nail the board to the dowels, then do the same with a second board.
Place the 6-inch piece of dowel so its center is at the center of one of these two boards--on the same side as the other dowels, running horizontally--and nail it in place. This will provide a ledge for your lamp to clip to.
Stand the two boards with the dowels upright, about 20 inches apart, keeping the dowel sides facing each other and the cut triangles facing down. Nail the two remaining boards to the sides of the dowels, forming a square base for your table with a dowel piece along each corner.
Sand all surfaces to remove splinters and loose wood. Sand the top edge as smooth as you can, wipe away any sawdust with a damp rag, then let the table base dry completely.
Paint the inside of the box with white latex paint, keeping the paint off the top edge. The white will help the light reflect more evenly within the table. Paint the outside of the box using latex paint in the color of your choice, again keeping the paint off the top edge. Allow the paint to dry completely.
Squeeze or paint a line of Plexiglas adhesive along the top edge of the table base and set a piece of 2-foot square Plexiglas on top of it for your table top, making sure it overhangs the table base as evenly as possible (about two inches) on each side. Make sure your adhesive is designed for Plexiglas or similar plastics. You may want to place something heavy, like a dictionary, on the table top to hold it in place while the adhesive dries.
Install a color-changing LED light bulb into a clip light. The best kind is the type with a metal reflector and a simple spring clip, available at most hardware stores, but any clip-on reading light that takes a standard size bulb may be used. Turn the table upside-down and clip the light to the 6-inch ledge inside the table base. Adjust the head of the lamp so it points toward the Plexiglas, then turn the table upright again.
Plug in the lamp cord and adjust the color-changing settings to suit your tastes.