doomsday uses both TCP and UDP for making network connections. If you are behind a firewall or you are using NAT, you must make sure that other computers are able to send network packets to your computer. This entails opening the appropriate incoming TCP/UDP ports on your firewall and/or configuring the NAT so that the correct ports are routed to your computer.
All the TCP/UDP ports that Doomsday will use (in a basic setup where there is either one server or one client on a computer) are visible in the network setup screens. The corresponding console variables are net-port-control (TCP) and net-port-data (UDP).
The server uses one TCP port for listening to incoming connections. By default this is 13209 (setting the port to zero will mean 13209 will be used instead). This port must be open for incoming TCP traffic.
The server also uses one UDP port of listening to incoming data messages from the clients. By default this is port 13209 (the same number as with TCP). This port must be open for incoming and outgoing UDP traffic.
The client uses one UDP port for data messages. By default this is 13209 (just like the server). This port must be open for incoming and outgoing UDP traffic.