Cut the dowel into four 6-inch lengths using the saw. Drill a 1/2-inch hole into the center of one end of four of the dowels using a drill bit slightly smaller in diameter than the 1/2-inch wood screws. Drill four holes into one of the flat surfaces of the bottom board -- one hole in each corner, 1/4 inch from each side. Position the four dowel segments with end holes over the holes in the bottom board and attach them together with wood screws.
Flip the lantern right-side up so the dowels are pointing into the air. Cut four 5-inch lengths from the dowel using the saw. Hold each length between the dowels of one side of the lantern, at the very top. Pre-drill holes into the sides of the side dowels and into the ends of the 5-inch dowels. Stagger the holes slightly so the screws will not encounter each other during the drilling. Attach the dowels together with wood screws.
Glue the glass tealight holder to the center of the rear board. Allow the glue to harden for one hour.
Position a piece of fabric on one of the lantern sides with its right side facing out. Staple it to the bottom board right near the edge of the board so the staples are not visible from the outside. Stretch the fabric tightly and staple it up the sides and on the top dowel rod as well. Repeat this process for all four sides.
Screw the two small eyehooks into the top surfaces of the lantern by hand, placing the eyehooks directly opposite from each other. Thread the picture wire through each hook and twist it in place securely. Hang in desired location.