The process you're looking for is like it's always been:
1. Open socket and connect to the peer using its IP address and port
2. Perform handshare (Send version, receive version and verack, send verack)
3. Push your tx in a tx message
The three message types and their structures on explained in the link you shared.
https://developer.bitcoin.org/reference/p2p_networking.html#version
https://developer.bitcoin.org/reference/p2p_networking.html#verack
https://developer.bitcoin.org/reference/p2p_networking.html#tx
FWIW protocol version 70016 introduced wtxid-based relay and nodes that have that version support this feature.