My child is the lucky recipient of some wonderful size 18 month hand-me-downs. I wanted to take a few of his short-sleeved polo shirts and convert them to long sleeves. Here's my little model showing off his new long sleeves:Here's some advice: Try to add on sleeves of an old short sleeved t-shirt so you don't have to hem the sleeves. I went through two different trials before successfully using t-shirt scraps.
As for sizing, I found that my child's shirts had 4" sleeves already; he needed about 10" total to cover his arms generously, so I cut 7" from a t-shirt. I zig zagged the sleeves (I don't have a serger, but if I did, I would've used it). Using t-shirt sleeves also allows the sleeve to ''taper'' to the wrist.This picture is with just plain knit (it was trial 1, not successful trial 3 with the t-shirt sleeves) without the hems, but you get the idea.Then, I pinned the sleeves to the inside of the polo shirt sleeve's binding (right sides together). I zig zagged this. I found the easiest way to sew this seam was to turn the whole thing inside out.
For this navy striped polo shirt (without the binding on the sleeve) I just pinned on the outside and tried to sew along the existing hem's seam.