Measure the table and mark off the exact center using a chalk line or yard stick and chalk or pencil.
Set up two sawhorses or attach two legs on either side of the center line with at least 5 inches between them.
Cut the table in half down the center line using a circular saw. Place the two halves side by side on the sawhorse or additional legs.
Mark spots for two holes along each freshly cut half; make them a good distance apart. Then drill 1/4-inch holes straight into the table top, parallel to the table top itself. Make them about an inch deep, or long enough for half of the wood peg to go inside.
Coat wood pegs in wood glue and insert them into the holes. Be sure they are straight and perfectly aligned; if not, redrill the holes a short distance apart. Do this for both halves of the table and drill holes that you leave empty across from each peg on each half, for when the table is closed.
Cut your leaf section from a thick piece of wood that matches your tabletop in thickness and width. If you can't find the right wood, glue two pieces of plywood together, or use fiberboard with a laminate that matches your table.
Hold the leaf to one half and mark off where the wood pegs will intersect the leaf. Do this for both sides of the table. Don't rely on measuring; mark the holes right from each half to each side of the leaf. Then drill holes into it and clear them of debris. Make the holes as deep as the pegs are long.
Attach metal slot braces, or a wood brace that overlaps the edge underneath the table on each half. This is a brace to hold the leaf, so make it sturdy. It doesn't need to swivel, as long as they don't hit each other when the table is closed and the leaf is removed. The slot or sliding braces must be longer than your leaf to allow you to remove it.
Insert the leaf and test your table.