Newbie wants to sell his car – how does that work?

Have a good day together. I hope that I am right here, because I want to sell my car first. And then buy another one. But in both I am absolutely Newbie. At the moment “my” car is still registered on my father, but I have vehicle registration, letter, keys and a written explanation about the change of owner. But the car would “eat” me if I switched to me. Insurance, the high fuel consumption – therefore I want to sell this car. But how does a sale like this happen? I want to offer the car via common portals, interested parties come by, at some point interested parties and I hopefully agree. At the moment, the car is still registered because I need it for emergencies. What if the interested person wants to have the car immediately and pays for it? I can download contracts on the net? Do I keep the license plates? Or who registers the car? How do I register with the insurance company that d he is sold car? In short: How am I on the safe side after handing over car and money is things authority and insurance? Well, that has no TÜV anymore, if that is important. Thank you for your attention!