This question is old, but I have sold a car this way before and don't see the method I used listed. This method is also probably better than the other methods in the case where the purchase amount is larger (closing on 5 figures or above) or if you simply don't feel comfortable carrying any large amount of cash around.
In my case, I arranged to meet the buyer at a bank we both had an account at. In the case you don't share a bank, for a large amount of several thousand dollars, even the hassle of opening a new account to facilitate the transfer can be preferable to some people. Once at the bank, tell the person who greets you what your intention is, namely that you are selling a vehicle, that you both have an account at the bank, and that you would like to transfer funds from the sellers account to the buyer's account. They may direct you to a teller or they may have a "personal banker" assist you with the transaction. How a particular bank does this may vary from bank to bank - they may require that the seller fills out a deposit slip and the buyer fills out a withdrawal slip after which they pull the money out, count it out, then deposit it back in the register, or they may have a more streamlined process. While they are doing this you can sign any necessary paperwork (e.g. the back of the title or whatever is needed in your state) and once they have confirmed everything is ready to go you can hand them the paperwork and keys.
In my case, once this was completed there was also an additional step that needed to be done at the DMV, so you may need to go there to finish things up. But really, if you are doing a multi-thousand dollar big purchase transaction like a vehicle there is no reason to not take a little extra time, go the extra mile (literally) if needed, and make sure everything is done right and everybody is happy.