How do you report hours that vary week to week?

I picked up part-time shifts as a quality inspector and I am confused about how to report them. I have been trying to stay organised about it. 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 3 months ago, and it got easier once I kept a simple log of every call and form.