Run two 1-by-3 1/2-by-36-inch MDF boards and two 1-by-3 1/2-by-17-inch MDF boards through a table saw, cutting a 1/4-inch wide groove that is 1/2-inch deep into one of the long, thin edges of the boards. Cut the grooves in the 17-inch boards all the way to the ends, but leave a 1-inch ungrooved section at each end of both 36-inch boards.
Position the four boards into a 24-by-36-inch rectangular frame. Slide one of the 36-inch boards out of the way and slide six 1/4-by-3-by-30-inch boards into the grooves in the 17-inch boards all the way through into the groove in the 36-inch board. Reposition the 36-inch board back into place.
Pull the two 36-inch frame boards away from the frame. Drill two mirrored holes into each board at each place where the boards meet, for a total of 16 drilled holes that match into eight pairs. Set a wood peg in each pair of holes, using 8 pegs. Push the frame back together to test the fit of the frame. Adjust the holes if necessary to ensure a snug, attractive fit.
Pull the 36-inch boards out again and place a dab of wood glue on each end of each wood peg. Run a small bead of wood glue along each spot where the frame boards meet. Push the frame boards back together and clamp them in place. Let the boards dry overnight.