Choose the Elastic
Choose elastic to purchase. A width of .5 inches is easier to work with than a thinner elastic, but .25 inches will be fairly easy to manage as well. Use the elastic to measure around the person who will wear the garment. Pull the elastic around the person's waist until there is enough elastic for a comfortable, but secure fit. Then, add 1 inch and cut the elastic to that length.
Iron the Waistline
Iron the garment into which you will place the elastic until it is smooth and flat. Fold down 1/4-inch of the fabric and press it down again to create a neat, crisp fold.
Sew the Casing
Fold the fabric down again in the same direction, creating a fold that is 1/2-inch wider than the width of the elastic you chose. Iron this fold as well. With a simple straight stitch, stitch the folded edge over the top of the garment it is resting on, stitching 1/8-inch from its edge.
Feed the Elastic Through
Pin a safety pin to the edge of the elastic and feed the elastic through the casing you created with the stitch. When the entire length of the elastic is inside the casing, secure the end of the elastic that does not have the safety pin to the fabric by stitching across the casing and back-stitching back off the fabric. Continue pushing the safety pin through, until the elastic circles the entire waist of the garment, and the safety pin comes out the other side of the casing. Remove the safety pin, and stitch across the casing again, securing the opposite end of the elastic. Hand stitch the opening closed with a needle and thread, keeping the stitching on the inside of the garment's waistband. Trim all loose threads.