Start with a "magic circle." If this is an unfamiliar term, go to YouTube and there are lots of folks that will show you just how to make one! Single Crochet 6 times into the circle and then tighten the loop. In the next row, chain one and make two single crochets in each single crochet! You'll have 12 single crochets when you finish the second round!
Keep making rows until the hat is the right size for your fairy! Sorry the photos aren't better, but I'm holding the camera with one hand and the teeny hat with the other!! Be sure to fit to your fairy until your hat is the right size! You won't need to put two single crochets in each stitch - just add the second single crochet when needed to have a rather flat circle.
When you do that final row in single crochet - without adding two single crochets in any stitch which keeps the shape flat - the shape of your little hat will curve under.