The process is varied depending on the venue used to sell the domain and where your domain is registered.
If you come to a deal on selling a domain privately (not through a broker or a listing service), you can use a number of different options. Paypal works for smaller transactions, but paypal doesn't offer much protection/support for domain name sales. An escrow service like escrow.com offers more protection but takes a bit more time and costs more in commission.
Transferring the domain is done through your control panel at your registrar. The process can vary depending on where you have the domain registered and whether you will be pushing the domain to an account at the same registrar or transferring it out to a new registrar. The process is simple once you get the hang of it (with major registrars anyways).
As for scams, familiarize yourself with the appraisal scam, learn the risks taken by using paypal and use common sense.
A general rule is that you push the domain after either getting paid or being notified that the money is in escrow.
Thank you for the in depth reply, it was exactly what I was looking for. I did check Google but a lot of the resources were dated so not sure if the same methods still applied.