After going through all of the pillbox hat tutorials I could find online, I chose How-to make a Pill(ar) Box by Laura aka Trudy4Life. The hat from this tutorial had exactly the look I wanted. Other advantages to this design are that it's rigid and won't lose its shape, and the elastic strap is easier to deal with than any of the other options I saw, which involved holding the hat in place with bobby pins or barrettes.
Using my glue gun and some cardboard support pieces cut from an empty cola carton, I created this little beauty:
The hat itself is made of red denim, which I got for free at a garage sale from a wonderful older woman who could no longer sew. She gave me several yards of this stuff and I've used it for many things over the years. The ribbon was the handle from a shopping bag. I cut the ends at an angle and used a tiny bit of nail polish to seal them so that they wouldn't fray. The button came from my big tin of buttons which once belonged to my grandmother.
I love this hat and am on the lookout for any excuse to wear it again.
If you like it as much as I do, I encourage you to make one. It's quick and retro chic, and doesn't require any sewing. Here are a few other photos to convince you.