A waistband casing consists of a tunnel sewn to accommodate a drawstring or elastic at the top of a skirt or pants and at the waistline of a dress.  A casing can also be used at the hems of sleeves and pants.  You will need to fold the fabric towards the wrong side and press about 0.75 cm (quarter-inch), then fold down again the width of the elastic or drawstring, plus about 1 cm (half an inch).  Sew the casing closed, all along the garment, leaving a 4 cm (2″) opening.  Optional:  You can also edgestitch all the way around the top of the casing.  This flattens out the gathers at the hemmed edge and neatens the look.

Bodkin with Drawstring
and Safety Pin with Elastic

Using either a bodkin or a safety-pin attached to one end of the elastic or drawstring, thread the item through, being careful not to pull the opposite end into the casing.  For an elastic, overlap the two ends about 1 cm (half-inch), sew together and insert back into casing.  Adjust gathers and sew the casing closed.  For a drawstring, you will need to insert two buttonholes, approximately 2 cm (1″) apart at the front of the garment, within the casing, in order for both ends of the drawstring to exit and be tied.  The buttonholes can be placed so that the drawstring exits at either the inside or the outside of the garment.

Waistbands with Elastic Casing (left) and Drawstring Casing (right)

You can also add a casing of different fabric, instead of folding down the fabric of the existing garment.  For this, you would do as above, but instead of adding the amount you calculated for the casing onto your original fabric, you would measure this amount onto the new fabric and cut it out.  You will also have to add another 0.5 cm (5/8″) or whatever is your seam allowance, as you will be attaching the casing to your garment.