The safest way to transfer a domain is to use an escrow service. It's important to ensure that the escrow service you choose is reputable. I'd recommend Escrow.com as one of the leaders in the industry, and they have escrow options specialized for domain name sales. Typically the buyers is expected to cover all escrow fees. I've used them before with success.

The basic process is that the buyer sends funds to the escrow service. The seller then initiates the domain name transfer with their registrar. Once the domain name is transferred, the buyer confirms this with the escrow service, which releases the funds to the seller. If the domain name is never transferred, the escrow service returns the funds to the buyer.

The transfer process goes fastest if you are both on the same registrar. Often, it's best to get the buyer to create a new account at the seller's Registrar.

There are also "Escrow Services" for very valuable domains, but I have never used one.