For the past 3 years I've saved up enough money to
buy a car, I have enough to pay it off all at once. I
don't need a loan so how does this work?
You pay for it and drive it home.
A vehicle purchase is just like any other purchase. Only difference is that you can negotiate the price first. Then make sure the seller has clear title to the car. If it is your first purchase, try to get a friend or relative to go with you as support. If buying from a private seller, meet in a public place such as a bank parking lot or police station.