I have a Better Homes & Gardens sewing book from 1961 that shows how to do this, but my camera died.
Here is a quick drawing:
To make the sleeve bigger, just slash through the center and spread. Take darts from the slash to the cap to make it lie flat. The darts just taper off and keep the armhole the same size. This can be done on short or long sleeves!
Also, I found this link to a blog, which might be helpful. She uses a different method.
I hope this helps you out! I haven't tried either method, so let me know.