How do you report hours that vary week to week?

I picked up part-time shifts as an event coordinator and I am confused about how to report them. This is my first time dealing with any of this. Pay posts on a different day from when I work. Do you report when you earned it or when you were paid?

Thanks for writing this out. I went through something close to it 5 months ago, and it settled down once I kept a simple log of every call and form.