How do you actually verify a used car before handing over cash?

I'm about to buy my first used car privately and the whole process makes me nervous, especially the part where you hand over a large sum and hope the seller was being honest. I keep hearing about people buying cars that turn out to have outstanding fines, bank loans, or accident damage that wasn't disclosed. I want to know what checks people actually do before committing, and whether there's a standard process or if everyone just wings it. I came across 800sayara.com/ while trying to work out where to start and it did clarify a few things, but I'd rather hear from people who've bought and sold privately. Do you insist on meeting at an RTA centre, do you check the chassis number against something, or is a test drive and a good feeling enough? I'd rather be the cautious buyer than the one who gets burned.