okay yvonne, i made a sample and took some pictures... hopefully these will help you make this hat! mine is miniature sized and done in double crochet... for the real hat i would do the hat portion in single crochet and the band in another pattern... maybe seed stitch.
so here's the hat part, worked up to where you want to start the band. i'd say that the band should be at least the bottom 2 inches of the hat.
now from here is where you make the chain to start your button band. i made mine long enough to cover about 1/6 of the hat circumference plus the chains needed for turning. mine is double crochet, so 3 turning chains, but for single crochet it is just 1
from here the band will be worked flat, so turn and start working back across that row until you get to the last chain for the band
now you are back to the hat portion... just keep working the row back around the whole hat
when you get to the last stitch of the hat portion, just stop there and it should look like this now
now make your turning chains, turn the work and start working back across the row
now you're back to the other end of the hat band
you can see how the band will fold over the other portion and be buttoned in place later
as for the buttonhole, i worked the next row in single crochet to show how i would do it. if you're using a different stitch for the band then make your fist few stitches in that. first work a few stitches of the hat band, then chain 2 or 3, depends on the size of the button you want to use
now skip the same number of stitches that you chained and keep working the rest in your pattern stitch. here's the finished buttonhole
then on the next row just work in the buttonhole chains as if they were normal stitches. continue working rows until the buttonband is as wide as you want.
hope that is a little clearer!