SIP routing relies on DNS lookups including NAPTR, SRV, and A records to determine the transport protocol, port, and IP address for a SIP request. The request URI and Route headers are used to determine where to send a request, while subsequent in-dialog requests follow the remote target and route set stored in the dialog state. Understanding SIP routing through RFC 3263 is essential for knowing how requests traverse the network and how responses follow the reverse path back.