Run two 1-by-3-by-24-inch boards and two 1-by-3-by-12-inch boards through a table saw to cut a 1/4-inch wide and 1/2-inch deep groove in the center of one of the long, thin sides of each board. Leave a 1/2-inch of ungrooved space at each end of each board. Arrange the four boards into a 18-by-24-inch rectangular frame with the grooved sections facing inward.
Move one of the longer boards out of the frame. Slide a 1/4-by-13-by-19-inch plywood board into the grooves of the frame. Reposition the frame back together.
Pull apart the frame sections and drill two mirrored holes into each point where the boards butt against each other so that there are 16 total holes. Put a wood peg in each pair of holes for a total of 8 pegs.
Apply a bead of glue to each end of each peg and a slight bead of glue between the boards that connect. Clamp the boards together overnight.
Rub the entire surface of the board, top and bottom, with a thin coating of linseed oil. Continue to rub the oil deeply into the table. Wipe until the table is smooth to the touch and not even slightly oily.