Cut the elastic into four equal lengths of 1 foot each.
Lay your fitted sheet out with the bottom side up.
Lay the center of one piece of elastic at the center of one of the corners--generally where the seam is sewn--and affix with a straight pin.
Measure 6 inches out from the corner of the sheet and mark with a fabric pen. Stretch the elastic out toward the pen mark so that it goes 3 inches beyond. Secure elastic with a straight pin at the point of the pen mark and two places between the pen mark and corner of the sheet. Repeat this step for the other side of the corner.
Starting at one end, sew the elastic to the sheet. Back-stitch a few times at each end to secure the elastic. Trim off the excess elastic and remove all pins.
Repeat the process for remaining three corners.