How do you report hours that vary week to week? - 7 months and counting

I picked up part-time shifts as an operations analyst and I am confused about how to report them. Sometimes my paycheck is late by a week. Do you report when you earned it or when you were paid?

Thanks for writing this out. I went through something close to it 7 months ago, and it settled down once I kept a simple log of every call and form.