I've gotten a few compliments, and I love compliments, on this one, so here's my first honest-to-goodness attempt to write a full pattern:
Gauge is approximately 5.5 sts/inch on size 4 needles with Paton's cotton yarn, but I knit loose so others would probably do better with size 5s. Because this was a hat for a new baby, head circumference 14 inches or so, I was much more comfortable on 4 dpns (knit with a fifth) than on a circular needle until I got to the two ruffle rows and BO at the end.
Cast 4 sts onto a dpn and work an I-cord (keep sliding the sts over at the end, like a typewriter) for 4 rows.
K1, M1 (I use the backward loop cast on, as suggested by Elizabeth Zimmerman; it seems counterintuitive, but it does not actually leave a big hole) add new needle, K1, M1, add new needle, K1, M1, K1, M1 (4 incs, 8 sts total, 2 on first two needles, 4 on third needle)
Knit 1 row plain
(K1, M1) around (16 sts total)
Knit 1 row plain
(K2, M1) around (24 sts) Here would probably be a good time to add the fourth dpn so that each needle now has 6 sts.
Knit 1 row plain
(It is fairly easy to identify the M1 stitch from two rows earlier, and right after that is where the new M1 will happen. It is also very easy to recognize the M1 st on the needle, so that helps keep straight whether it is an inc row or a straight row.)
Continue to repeat these two rows (next will be K3, M1 around) until you get to K7, M1. After this row you will have 80 sts, and that is the total needed for the new baby hat. If you want a larger hat, keep increasing at the eight points.*
Keep knitting around until hat measures 4 inches from last increase (if you're making the hat for a larger size head, you probably need 5 or 6 inches). The easiest way to end a hat like this is a roll brim, which would involve about 8-10 more rows and the binding off, but if you would like a ruffle, get out a hat-sized circular needle, K1, place marker, KFB, [K1, KFB] around. You'll know you're done when you have 1 st before the marker.
Next row: K1, slip marker, KFB, [K1, KFB] around.
Next row: BO.
That's pretty much it. Add stripes and Fair Isle designs at your whim.
*This is pretty much how I make all my top-down hats, either starting with 4 sts, and then making 8 points of increase or starting with 3 sts and making 6 points of increase. I like the way the I-cord looks, and I guess I like increasing a tiny bit better than decreasing. I would say that there seems to be a more pronounced danger of making the hats too fat and droopy this way, and that it can be a slight pain if you're doing earflaps, but I just love the feeling of starting with such a small number of stitches and watching the knitted fabric grow.
I started doing hats top-down instead of bottom-up partly because I was so enchanted with dpns and partly because I believed that I wouldn't need to do a gauge swatch because I'd know how many sts I had to the inch before I needed to stop increasing. I'm not sure that's true. but I will probably continue to make hats this way.
Abbreviations, in order of appearance: sts=stitches; dpn=double-pointed needles; BO=bind off; K=knit; M1=make 1; inc=increase, KFB=knit into the front of the stitch but don't slode it off the needle; knit into the back and now slide it off (1 st inc)