When you have the clear title, as you noted, then things are simpler. There’s no lien to be satisfied, and you can make a clean transfer.
Your state DMV should explain the process – in sometimes excruciating detail – but it’s usually pretty straightforward. It’s worthwhile checking with your state rules, because they all have different rules. (Trust me on this; I’ve bought and sold cars in several states, and the rules always vary from one to another.)
In general, however, when you have the title, you’ll notice that there should be a “transfer of ownership” section on the back. You and the seller will fill that out and you’ll sign the vehicle (and title) over to the new owner. He’ll take that paperwork – including the car registration, which you may also have to sign over, or perhaps just “give to” the new owner as part of the transfer – to get a new title in his name only, and to register the vehicle.
In some states he will also have to pay a tax based on the value of the transfer, so some buyers may (illegally) request that you note a lower sales price on the title, because it will reduce their tax. I’ll leave that between you and your conscience; just remember that the title is a legal document, and falsifying legal documents generally carries a penalty, if that’s discovered. (That particular infraction is seldom discovered, but still…)
Talk to your insurer about cancellation.
If you’re going to buy a new car, then you may not want to cancel, just transfer, and as long as they’re aware of the transfer then it’s generally no problem (or extra cost) to cover both vehicles for the short time until the transfer to new ownership is complete. And I generally recommend that you do that, just in case the transfer falls through at some point where you thought, for example, that the buyer had given you a good check, but it bounced, or some other defect in the transaction keeps the vehicle in your hands… even if the “new owner” is driving it. You don’t want to be uncovered if you still have any interest in the vehicle. Again, the risks are generally small, but…
@zenvelo‘s point about “safe spaces” is good, too. In the olden days we didn’t worry too much about having folks come by the house to look at the vehicle in our own driveway. After all, the person viewing the car was more than likely from our town anyway, and had seen the car advertised in the local newspaper, or with a sign pasted on it in our own front yard. These days things have changed. It’s a good idea to have the vehicle shown and transacted in a public, safe place away from your home, unless you know the buyer personally.
Also, as part of the transaction process, and depending on the value of the vehicle, it’s a tossup whether check or cash is safer. I’ve never been burned by accepting a check when I can verify the person’s ID from a valid driver’s license, but that can be iffy… and accepting cash carries its own risk, because of the prevalence of good-quality counterfeit bills and because having a lot of cash on your person is always somewhat risky.