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Connecting to ZNC
You connect to znc using any ordinary irc client. You may configure your znc account via irc commands. You may find it a lot easier however to configure your networks and settings using the Web configuration module. In which case, you would navigate to http://znc.example.com:6667 or https://znc.example.com:6697 depending on your port/ssl configuration.
If you have multiple irc networks setup under your znc account, you may connect to a specific one directly by adding /networkname to your username like so
Connecting to Multiple Networks
Unless you have a very old version (in which case you should UPGRADE IMMEDIATELY), one user with TWO NETWORKS configured (NOT an additional server specified in the same network) and two connections, one to each network, authenticating with zncuser/zncnetwork:password is what you need
Create another network, name it whatever you like (for example "freenode"), and add the irc server address to the network, Then authenticate with /a separate irc connection/ to zncuser/freenode:yourpassword