Conquackulations on your sale....
If the domain name is not registered with a service that allows paperless transfers, such as Enom resellers and Dotster resellers, like DomainDuck (quack), I suggest you get such an account, which is simple and then initiate a domain name transfer from your current service to your new service. That might take 1-3 days if all goes right.
For payment, if the price is not too high, $1,000 for example, you can set up a PayPal account, if you don't already have one, which allows secure credit card payment over the Net. Personally, I use ClickBank.com for this, but the rules are different than PayPal.
With your domain name transferred to a paperless service and a credit card account, you can do the actual payment and transfer in a matter of minutes... No paperwork!
If the selling price is higher than $1,000, or if your buyer prefers, you can use Escrow.com, but I have no experience with them. Many others here on the forum do.
Hope this answers your questions.
quack