The official Trosnoth web server runs on play.trosnoth.org. When you install Trosnoth, it is configured to use this server by default.
To play Trosnoth well, you need to work together with your team, which can be difficult over the internet. To help with this, there is a Mumble server running on play.trosnoth.org.
If you want to hear about (or organise) online matches or tournaments, you may want to join the Trosnoth players group.