This manual assumed you are running a singe-site contest; that is, the teams are located closely together, probably in a single physical location. In a multi-site or distributed contest, teams from several remote locations use the same DOMjudge installation. An example is a national contest where teams can participate at their local institution.
DOMjudge supports such a setup on the condition that a central installation of DOMjudge is used to which the teams connect over the internet. It is here where all submission processing and judging takes place. Because DOMjudge uses a web interface for all interactions, teams and judges will interface with the system just as if it were local. Still, there are some specific considerations for a multi-site contest.
Network: there must be a relatively reliable network connection between the locations and the central DOMjudge installation, because teams cannot submit or query the scoreboard if the network is down. Because of traversing an unsecured network, you may want to consider HTTPS for encrypting the traffic. If you want to limit internet access, it must be done in such a way that the remote DOMjudge installation can still be reached.
Team authentication: the IP-based authentication will still work as long as each team workstation has a different public IP address. If some teams are behind a NAT-router and thus all present themselves to DOMjudge with the same IP-address, another authentication scheme must be used (e.g. PHP sessions).
Judges: if the people reviewing the submissions will be located remotely as well, it's important to agree beforehand on who-does-what, using the submissions claim feature and how responding to incoming clarification requests is handled. Having a shared chat/IM channel may help when unexpected issues arise.
Scoreboard: by default DOMjudge presents all teams in the same scoreboard. Per-site scoreboards can be implemented either by using team categories or team affiliations in combination with the scoreboard filtering option.