Trousers with elastic waistbands are easy to wear and nearly as easy to sew. If you can make a straight stitch with a sewing machine, you can put elastic into trousers. You simply have to insert the elastic through a casing that you've made by folding and sewing the top of trousers.
With the inside of the trousers facing you, fold over the top edge 1/4-inch. Press. Fold over again to create a 1 1/4-inch casing from the top folded edge to the bottom folded edge. Press. Insert straight pins every few inches to hold the casing in place.
Sew a straight stitch around the entire top edge, 1/8-inch down from the fold. Sew around the bottom of the casing as you did for the top, but begin and end your stitching 1 inch away from the back seam of the trousers. This will leave a 2-inch opening through which you will insert your elastic.
Cut a piece of elastic equal to the measurement of the wearer's waist minus 2 inches. Insert a safety pin into one end of the elastic. Put the closed safety pin into the opening of the waistband. Push and pull the pin to work it through the casing. When the elastic is almost all the way through the casing, use a straight pin to attach the other end of the elastic to the trousers near the casing opening. This will prevent the end from accidentally being pulled all the way through the waistband. Bring the safety pin out through the casing opening.
Check to make sure the elastic did not become twisted when you worked it through the casing. Straighten it if necessary. Grasp both ends of the elastic and remove the pins. Overlap the ends of the elastic 1/2-inch. Stitch two parallel lines across the width of the overlapped elastic to hold the ends together. Release the elastic to allow it to snap into the casing.
Pin the casing closed, smoothing the fabric to ensure it is not bunched. Sew across the 2-inch opening to complete the stitching line at the bottom folded edge of the casing.