Freelance Caregiving: How to Cover Legal Bases?

Hey all, I'm a professional caregiver employed by a private company in America. My friend recently offered to pay me out of pocket to care for their grandfather. I've never gotten this kind of offer before, and I'm scared that this form of employment could backfire on me (e.g. he slips and falls while I'm on the clock, I get sued for everything I'm worth) Obviously I'm not planning to care for him incompetently, but you can never be sure what's going to happen. How do I make sure I'm not agreeing to anything that could make me liable for any harm that could occur on my watch?