It's best to cut a pattern with your measurements first so that you properly cut your fabric. You don't want to accidentally cut your fabric too small and end up ruining your skirt.
There are many free patterns patterns on the web. There are also craft stores that have books that illustrate how to crochet. If you are a beginner, keep it simple...
There are lots of free hat patterns on Ravelry. You can also just search "Beanie button hat free pattern" on an internet browser and it should show up.
It's virtually impossible to cut a pattern from just a photo and make it exact. I would recommend printing it out then cutting. However, make sure the measurements are right.
