Having made a few of these caps at this point, I've realized that many of the patterns follow a similar basic form. Since I've been using different yarns from my stash (using only nonwools and very soft ones b/c these are chemo caps), I've adapted to the diff. gauges of the yarns, and thought I'd share.
Choose the recommended needle size for your yarn - you need a circular needle and a set of double pointed needles in the same size.
Cast on the circular needles enough stitches to fit the circumference of the head you are making the hat for (note there will be some give in your band and so, stretch your cast on line a little as you measure for the circumference (esp if you cast on like I do with very tight very close together stitches).
knit back and forth on your circular needle (unjoined) with a basic stitch for the brim. This can be a rib (K2P2) or a garter (just knit back and forth) or a moss stitch (K1P1) or anything you want. You have a long thin rectangle going at this point.
When your brim reaches approximately 2", join your knitting and continue knitting in the round until your knitted piece reaches 6" from your cast on row (or 7" or 8" if you're working with bigger heads). (NOTE: most patterns say put a sitch marker to mark the beginning of the row here, moving the marker up each time you start a new row. But I realized I always joined 2" above where I initially cast on - where there was always an unwoven in tail , I had a natural built in marker so I don't add another. But if it helps you, by all means, add the marker before you join). I normally use stockinette stitch here, but again, anything would work... Just keep it in a pattern that would stretch a bit. (a rib works well too). Since you're knitting in the round at this point, stockinette is just straight knit stitches and it is a very nice "I don't have to think too much about it" knitting.
Once you get to the 6" (or 7" or 8"...) transfer your project to double pointed needles, evenly distributed among the needles. Now you start to decrease (and form the top of the hat). Knitting in the round:
[K8, K2Tog]. repeat til end.
[K7, K2Tog] repeat til end
[K6, K2Tog] repeat til end
[K5, K2Tog] repeat til end
[K4, K2Tog] repeat til end
[K3, K2Tog] repeat til end
[K2, K2Tog] repeat til end
[K1, K2Tog] repeat til end
K2Tog, repeat til end
Now, cut the yarn from the skein, giving yourself about a 8" tail. Thread a needle through the end, and then run that needle through all the remaining stitches on your needles, pulling tight.
You're done. Join the loose ends of your brim, add a flower, a button, etc. Weave in all yarn tails.
Here are three more that I just finished for a very special little girl. That's five total, as a girl cannot have too many choices, eh? The pinks are cotton; the white is microspun with yellow crochet thread accent for a butter yellow hat. TFL. Wendy