Reporting part-time earnings while on benefits

I picked up part-time shifts as an event coordinator and I am confused about how to report them. This is my first time dealing with any of this. The form asks for gross earnings, which I do not see until later. Who can I ask without risking my claim?

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