This tutorial describes how to do small pretty icons using paths. The tutorial requires some prior knowledge of paths - but not much.
<- The result! Not much eh?
See Christina's gallery to see some hats done via this technique.
Create a new image of quite big proportions. For the crown I used a canvas which was 700x500 pixels, but that is a bit oversized. Less will do too. Find the paths tab in the layers dialogue (Control-l).
You should create a new path for each path you do. I used two paths for the crown. You create a path by pressing the single sheet of paper in the paths editing (New path). I used one for the crown, and one for the band across it.
Start each path by clicking out all the point, to create a very straight looking image.
Do not(!) worry about getting the lines nice and bendy before you path'ed out the entire path. There will be plenty of time to adjust later. Try pressing the little black dots once the path is ended. This will allow adjusting the curves. You can also adjust only a single of the two lines by pressing shift. It is easier to comprehend if you just try it (Yes! Go do it!)
You should be able to achieve something nice and smooth like this
You can lock a path by pressing next to it in the dialogue to prevent further modifications.