How do you report hours that vary week to week? - 8 months and counting

I picked up part-time shifts as a payroll clerk and I am confused about how to report them. I have read a lot of threads here and could not find my exact situation. Pay posts on a different day from when I work. Did anyone get an overpayment notice from a mistake?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.