How do you report hours that vary week to week? - any advice?

I picked up part-time shifts as a marketing coordinator and I am confused about how to report them. I worked as a marketing coordinator before this. Sometimes my paycheck is late by a week. Who can I ask without risking my claim?

Thanks for writing this out. I went through something close to it 6 months ago, and it settled down once I kept a simple log of every call and form.