(Warning: Amateurish photography)
I found an adorable slouchy hat on Pinterest and thought I'd give it a go. In my opinion, the photo of the purple hat, and the directions given, bear not the slightest resemblance to each other. It's a good thing I'm rather innovative when I crochet, or this would have been a disaster. (In other words, the blogger's directions are useless, especially at the hat band.)
Use a J hook and worsted weight yarn. Begin with a magic circle. Here's a youtube tutorial for that, if you need it. I think a magic circle is the best method to begin a round crochet project like this. Put 6 single crochets on your circle. Add 5 more rows of single crochet, putting two dc's in each stitch from the previous row when possible, without buckling your work. It should be tight, but stay flat with some pressing. I made mine too tight.
The band: I switched back to my J hook. I started by working a dc in each stitch from the previous row, pulling the tension on my yarn a little with each stitch to help "tighten up" the hat a bit and rein in those floppy tc's -- I did that for one row. On the next row, I did single crochets, working only every other stitch; this was the row when I was trying to reduce the hat's brim to the right size for my head. Try it on several times so you don't reduce too much.
Once you get the edge the right size, you can add a nice band. I decided to do 2 rows of alternating front- and back-post double crochets, to give it a ribbed effect.
This is the same Simply Soft red yarn I used for the bobble stitch ear warmers, and the drapey shawl.