If you're following the A-line dress tutorial, you'll pick up right before the step where you sew the sides of the dress up. Cut out two strips of contrasting fabric that is 3 inches x the width of your sleeves.
Sew this to the end of the sleeve, right sides together.
Fold edge of contrasting fabric over 1/4 inch and press. (Sorry for the funky coloring in the photo!)
NOW sew up the sides of the dress and the bottoms of the sleeves. Zig-zag to finish. You'll notice that you don't have to zig-zag all the way to the edge since you'll be folding it over.
Fold contrasting fabric over and press.
I didn't take a pic of this, but put a few pins in there to keep it in place. Now here's the only kinda tricky part. If your sleeve isn't wide enough, the sleeve won't fit over the arm of the machine. That's fine; mine wasn't. You just have to make sure that you don't catch the other side of the sleeve as you're sewing. My best advice: take your time!!
Stitch close to the edge of the contrasting fabric. Go all the way around the sleeve, leaving a 1/2 inch opening.
Then sew another line of stitches about 1/2 inch from that first one. I just estimated it. Go all the way around on this one; no need to leave an opening. This is the casing for your elastic.
Cut two pieces of elastic that are 2 inches shorter than your original sleeve width (my sleeves were 12 inches wide, so my elastic was 10 inches). Thread it through your casing, using a safety pin.
Then stitch the two ends of the elastic together. I do a nice messy job. :) It doesn't have to be pretty; it just has to hold.
Finish stitching up your casing, and you're done!