Would I need to use some network library? if so what are good ones?
Basically everything that I would need...
I know I would need a network connection(i think that's called socket or something) also a lot of text boxes: user in chat, chat that's coming in, and input text.
What else would I need to make this a nice functional irc chat client... And once again how would I go about it.
The GUI part depends on which framework you're using. Using Qt and Qt Creator is probably the easiest way.
Qt also provides network functionality (see the QTcpSocket class), so you're all set.
Other than Qt, there are other network libraries such as Boost.Asio. You could even write a simple C++ wrapper for your operating system's socket functions if you are so inclined.
Aside from that, you'll need to read a bit about the IRC protocol.