How I did it:
1. Carefully cut the long sleeve from the shirt. There will be a fat, serged seam around the arm hole. Be sure to cut towards the body side so you have a clean edge at the arm hole.
2. Keep your finger on the other side, so you can 'feel' where you are cutting. If the fabric bunches up, you can easily cut an unintended gash in the arm hole.
3. You should end up with a nice, clean arm hole.
4. Measure the diameter of the sleeve with a tape measure. This does not have to be perfect.. just a general idea of diameter. In this case, the diameter is about 14 inches (7" x 2). I'll be using a 1/4 inch seam allowance, so I need at least 15 or 16 inches of sleeve material. A little more is okay, as you will see when we set in the sleeve.
5. Measure the sleeve, so you know what you have to work with. Fold the sleeve as shown. Measure across the bottom of the sleeve, from the fold to the end of the curved part. This is approximately 9 inches, so when it is opened, I will have 18 inches of length. This is more than the 16 inches I estimated above, and that is enough. (Plan B would be to make the sleeves out of different fabric)
6. Cut the sleeve as noted by the black line. It is about 4 inches wide.
7. Unfold and you will have an oblong piece of fabric that is about 8 inches wide and 18 inches long. Cut in half to yield two pieces that look like this.
8. Sew a rolled edge on the curved part of each sleeve. To make this easier, I used wash-away spray stabilizer. I covered all but 1/8th inch of the curved edge with paper and gave the exposed edge a quick spray. You can just sew and fold as you go, if you don't have any stabilizer. It will take you longer, but it will work. For curves, I fold both ways into the curve to help keep it smoother.
10. With right-sides together, sew the sleeve together at the small ends, using a 1/4 inch seam allowance. Mark the center of the sleeve (this will be used to match up with the shoulder seam).
11. Set in your sleeve. Right sides together, place the sleeve into the arm hole and pin. Match up seems at the arm pit. Note that the serged seam will fold one way. Fold the 1/4 seam allowance the other way. Pin.
12. Match the shoulder seam with the center mark on your sleeve. Pin. Starting at the bottom, pin sleeve all the way around until about an inch from the top on either side. There will be excess sleeve fabric. Don't worry about it yet.
13. When you get to the top, you may have a little excess.
14. Make a little pleat right at the top shoulder seam and pin. This is the completely pinned sleeve.
15. Sew in the sleeve. Use a 1/4 inch seam allowance. I start an inch behind the armpit seam. I like to get a running start to get over that little hump.
16. Be sure to keep your fabric straight. Knits like to roll up. I keep my fingers under the edge to make sure they are straight in the right place.
17. Repeat with other sleeve. Snip loose threads and turn right-side-out.
18. Voila! A capped-sleeve night shirt. Present to your daughter who will say "Gee Mom, I really wanted the sleeves more ruffly than that". Astute observers may note that I only used one long sleeve to make both cap sleeves and that I could have opened up both sleeves, sewn them together and then would have had plenty of fabric to make a nice gather at the shoulder for more ruffled cap sleeves. Please don't tell my daughter.
I hope this tutorial will be helpful to someone (anyone!). It's my first try at an illustrated 'how to' and it actually took me longer to post it than it did to do the alteration.