Reporting part-time earnings while on benefits

I picked up part-time shifts as a mechanic and I am confused about how to report them. I am in Raleigh, in case local advice matters. 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 last year, and it got easier once I kept a simple log of every call and form.