I had a skein of hand spun yarn (mine) that I wanted to get rid of and didn't really know what to do with it. I didn't know what gauge it would work up to, and I don't like swatches, so I decided to do a top-down earflap hat like one I published earlier on this blog. But once the increases were finished it looked kind of boring, so I did a row or two — three, really — of purl, and another three rows of knit... And then finished with a rolled hem. I really like it. So here's an attempt to write down what I did.
Cast on 6 stitches. I used a circular cast on that I kind of figured out, but really Emily Ocker's circular cast on is great.
Transfer the stitches to a longish circular needle, increasing in each stitch as you go. That gives you 12 stitches. I used the magic loop technique, so I had the loop pulled through so there were 6 stitches on each side.
K1, inc in the next stitch all the way around.
Knit one row,
K2, inc in the next stitch all the way around.
Knit one row.
Keep on going like this, increasing in the stitch above the increase bar on every second row, until the increase section is long enough: about 3.25 inches for a child's hat, 3. 5 for a woman's, 3.75 to 4 inches for a man's.
Now begin the straight section, where you'll get the accordion effect. You can change to 16" circulars if you prefer, or keep on using magic loop.
Knit 3 rows.
Purl 3 rows.
Keep on like this until the straight part is long enough. If you can, measure the target head from the top to the earlobes. Or longer if you want a slouchy hat.
When you have done enough, change to slightly smaller needles and knit 5 - 10 rows until the rolled edge suits your tastes. Then cast off, not too tightly.
Your materials will depend on the yarn you're using. My handspun was sort of bulky, so I used 5 mm needles. My medium-sized hat took 90 g of yarn. But YMMV (your mileage may vary).