Separate the table at its center. You may be able to pull one side to effect this; or you might need a second pair of hands so each of you can pull one-half of the oval table.
Lay the leaf neatly into the space between the two table halves. Be sure the outside edges of the leaf are flush with the outside edges of the table's top halves.
Re-close the table by sliding the two halves back toward the newly-placed center leaf.
Look just beneath the table top at each end of the table to spy the pull-out leaves.
Ease each leaf out from beneath the table until it is fully revealed.
Pull the leaf gently upward, allowing it to become flush with the table top.
Release the pressure on the leaf. You should hear it snap or click into place.