I have a caregiver. I don’t want to go through an agency. What I’m trying to find out is how can they get paid?

Make sure the tax requirements are fulfilled when you pay the caregiver. You can consult with an accountant to find out what is required and how to handle it.

They get paid by you. I would use check.

I personally would pay them via check with a memo in the check what the payment is for, and I would make a copy of said check. I think that is a good paper trail to prove you are paying for a specific service. Remember to check IRS rules.
You may find this easier if you use a caregiver agency, but it would also cost you more.
Best of luck.

If you have the funds, you pay them. The the other option is in home Medicaid. Its for low income people who fit the criteria. Make an appointment with your Social Services.

They get paid by you.