IRC is short for Internet Relay Chat, a network protocol for chat. The preferred way to connect to IRC is with an IRC client, although there are web IRC clients available. search google for "IRC client" or "IRC web client".
A "nick" is an IRC name.
Channel names start with "#", trillek is on channel "#project-trillek"
irc.freenode.net is the address for the IRC service Trillek uses.
IRC clients use commands that start with "/"