Transfer draws more questions than any other step in a sale. In practice there are two flows and both are predictable.
For generic extensions (.com, .net, .org) the process runs on an auth code. The seller unlocks the domain and sends you an authorisation code, you enter it at your own registrar, and you click the confirmation email. Registrar approval windows run up to five days; in practice it usually closes in two or three.
For Turkish extensions (.com.tr, .tr, .net.tr) the process runs through nic.tr. The buyer needs a nic.tr account. The seller opens the transfer request and the buyer approves it from their own panel. Since the document requirement was dropped in 2022, no extra paperwork is needed.
The critical point is the same in both flows: payment shouldn't be released until the transfer completes. That's what the escrow structure is for. If the transfer fails, the buyer gets the money back and the seller keeps the domain.