There are a few approaches available here. The most obvious might be to use threads - one thread that would read from the socket (blocking), a second thread to write to the socket (blocks on the input queue used to feed it stuff to send), and a third to read from stdin (perhaps using Term::ReadLine). I'm not sure if that middle thread is quite needed, though it would handle race conditions between the first and last threads for sending stuff to the IRC server.
Personally, I do this basic type of thing with a single thread using event-based code, usually AnyEvent/Coro, though some will swear by POE. And, with a new enough Term::ReadLine, you can integrate it with Coro fairly well, or other event loops not quite so well, but still passably if done with Term::ReadLine being your main event loop (see Term::ReadLine::Event for example code), though there's always the issue of spitting stuff to the screen (input from IRC server) while waiting at a prompt.
That's for "this basic type of thing." For this specific type of thing (IRC), I use Xchat and perl plugins to Xchat.