Like I said, this is constructed from sleeves. Two of them. If you're using a shirt with short sleeves you may be able to skip the second half of this, but in my case I was using the top half of sweater sleeves, so I had to pick my brain and figure out how to finish it off. But we'll get to that in a sec.
Eh, you like that? ...ok, sorry. I tried. Follow the diagram, if you can. First you want to cut the sleeves off, and then open up the seam that closes the arm together. You'll have two pieces that are shaped like the third picture. Cut about an inch off the top (keep in mind; my sleeve pieces were about 8 inches long before I cut that off, so if yours are shorter you may need to cut less. If they're longer, cut some off the bottom too.) Put them right sides together and sew up both sides. Then finish off the top the same way we've done before.
Now you should be left with something like this:
Alright. Here's where it gets hairy.
We're going to add elastic! If you've ever made a skirt with an exposed elastic waistband, then you know where I'm going with this. If not, good luck! (Just kidding. It's not hard, but it's definitely going to test your patience if this is your first go at it.)
Start by cutting a piece of elastic that will fit comfortably around your head; tight enough to stay on, but loose enough to wear for long periods of time without getting a headache. Once you have the elastic cut, measure it, and mark the quarter, half, and three-quarter points on it. Then, sew those points to the corresponding points inside your hat. (Fold the edge over about ¼ inch, and just sew a zig-zag line across the width to keep the elastic in place; see the top picture.)
Now you finish it up by sewing the elastic all the way around the inside of the hat. Use a large zig-zag, and sew the ¼ inch piece of the hat that folded over to the edge of the elastic. It's a little easier if you work in fourths, going from one of the points you already sewed to the next, while keeping the elastic stretched all the way out. (This is the hardest part, and it may take some trial and error, so if you're not comfortable with the process, practice on some scrap fabric first.)
And now you are the proud owner of a scrap hat, that can be worn pulled down over your ears on cold days, and pushed back like a head band inside. :) Woo!