Cut a dado across the end grain on each end of your assembled tabletop. Do this on both the top and bottom of the tabletop, forming a long tongue on each end of the top. The depth of the dado should be equal to 1/3 the tabletop's thickness. The width may vary; 3/4 inch is a common dimension.
Cut the material for the breadboard ends to the width of the tabletop. This material should be the same thickness as the tabletop and 2 to 3 inches wide.
Cut a groove into the breadboard ends. Using the table saw, cut a groove centered in one edge of each breadboard end. The width of this groove should be equal to the thickness of the tongue you've cut on the tabletop. The depth of the cut should equal the width of the tongue.
Assemble the ends by sliding the grooved edge of the breadboard end over the tongue on the tabletop. The joint should be tight; a little tap from the hammer may be needed, but don't force the pieces together.
Fasten each breadboard end with a single nail. Select a nail slightly shorter than the thickness of the tabletop. Put the nail through the center of the joint, nailing from the bottom so as to hide the nail. Using only one nail in the center allows the tabletop to expand and contract without splitting.