Make a square with the four pieces of 1-by-4 inch boards. Place the 14-1/2-inch pieces on the inner edges of the longer pieces and hammer together with brads at each joint.
Place one 2-by-2 into a corner of the square and check that the top of the 2-by-2 is flush with the top of the square. Apply wood glue to the two sides of the 2-by-2 that will touch the inside of the square. Nail brads through the outside of the square into the 2-by-2 leg. Repeat for the other three legs.
Place a 1-by-1-by-11-1/2 in between two of the legs along the 14-1/2 inch side of the square. Apply wood glue and nail in brads through the cleat into the square. Repeat with the other 11-1/2 inch cleat.
Place the remaining cleats in between the legs on the 16-inch sides of the square. Apply wood glue and nail brads through the cleat into the square.
Place the top of the table right-side down and place the square with the legs attached on top of it with the legs pointing upward. Nail brads through the 1-by-1 inch cleats into the table top.
Fill the holes in with wood putty and allow to dry according to the package directions.
Sand the entire table with a hand sander and apply paint or stain as desired.