What's the process of buying a car off of someone privately?

There a plenty of tutorials on YouTube.

>After I get the car, do I just go to the DMV with the paperwork and go from there?

Pretty much. After you buy it and both parties sign the title, you will want to go straight to the DMV and get it in your name. Depending on your location you might need insurance to do anything so if that's the case for you have your policy number or proof of insurance with you.

>>18628049
Get their ID so you have some protection from a scammer.

Look at the title first. If there is a loan (lien) on the car, it has to be paid off first and usually a new title issued in just the sellers name (with no lien on the vehicle).

Get a bill of sale. If you can, do the exchange at your bank and have someone at the bank review and notarize the seller's signature on the bill of sale.

If the seller insists on cash only, take someone with you so you don't end up without the cash and without the car.