Measure your placket. This is the part of the cuff that attaches to the opening on the sleeve of the shirt. It's also where the shirt buttons close. The placket has two parts: the skinny rectangular side and the wider side that has one pointed end and a button hole.
Begin at the wrist and cut a slit up the sleeve of your shirt that is the same length as your placket.
Pin the skinny half of the placket to the bottom half of the slit.
Topstitch the placket to the shirt. This means stitching the placket on the right side of the garment as opposed to turning the sleeve inside out and stitching on the inside of the sleeve. Topstitching is a great way to accent the lines of a shirt.
Pin the other half of the placket to the other half of the slit in your sleeve. The pointed end of the placket should be pointed toward the armpit of the sleeve.
Topstitch the placket onto the sleeve.
Line up the cuff with the sleeve.
Pleat the sleeve to fit the size of the cuff.
Baste, or hand sew, a stitch into each pleat to hold it in place.
Pin the right side of the cuff to the right side of your sleeve. Leave 1/2 inch of sleeve for seam allowance.
Turn your shirt inside out.
Stitch the cuff to the sleeve.
Repeat Steps 1 through 13 with your other sleeve.