Using worsted or bulky yarn, your choice, chain enough stitches to make 9 inches long plus 3 ch for turning.
Turn, half double crochet or single crochet across the row. Double crochet unless in a brushed yarn seems to be a bit gappy and not so warm. You can do any stitch you wish so long as the dimensions equal 9x18 inches.
Continue rows until work measures 18-19 1/2 " in length.
Cut yarn, leaving a tail 2 ft. long. Using this sew up the side seam, the short side, making a wide "tube".
Using yarn needle now take the same yarn tail and make large stitches around one end of the tube. This is to pull it in and gather it. Do this, secure it shut, knot the yarn, trim yarn tail to a few inches and weave in end.
You now have a basic hat that if made slightly wider, say 10-11 inches, will have a roll-up brim.
If you wish you can do the rectangle "the other way around". Start with a crochet chain of 18" in length, plus 3, turn and crochet back and forth across this until the work measures 9-10" in length. You still sew up the shorter two sides together, it just means your stitches will go across the hat not up and down it. :)
The stitch used and the yarn weight used is up to you of course. Single crochet in back loops only makes it quite stretchy. The warmer and less gappy the better. I've done a few hats in the alternating dc, sc pattern. It works up fast and isn't gappy at all. :) Happy hooking!