How can I hire a caregiver for my grandma under private pay?

You can call a Home Health Care Agency and ask them to provide caregivers for you to interview. They will most likely have a contract for you to sign.

An alternative is to put an ad in your local paper and do the interviews (and intense background checks) yourself. There is a Caregiver Agreement on this site that you can both fill out and I’d suggest having an attorney help you and witness or notarize it. You will have to consult your financial advisor to help you with taxes.