Do you have to file paperwork each month on being someone's guardian?

The protocol may differ from state to state, so I would contact the courts or an elder law attorney in the state where the person resides.

Guardianship is given by the Court. My brother reported once a year.

I would think there is something in paperwork on when and how you need to file.

Taking on guardianship is not to be done likely, and you would need more answers to more questions than can be done on the forum. I would say you need to check with an elder care attorney in your state if this is something you intend to do. For children's estates you often have to do it a month from taking on, and then every two years. In the case of an elder you would likely have to file with Social Security to become representative payee. That is yearly filing. Record keeping must be meticulous if you are managing money. This is a HUGE task. I would learn all about it before agreeing to do it.