Magic pretty much said it. You're gonna need ircd software (internet relay chat daemon), some sort of services software (there are many, but certain ones are for certain ircds), a box that this can be hosted on (preferably *nix) ... and preferably some sort of (sub)domain name to point to the IP(s) of the server(s) running the ircd software. I myself use Nefarious ircd (basically ircu) and x3 services (based off of srvx) ... you can find info on both of those
here. You would need to purchase the domain name, unless you were to use FreeDNS, and if you wanted someone else to host your ircd and services then youd need to pay for an ircd shell with at least one BG process for your use (obviously for services). You'd have to (up|down)load the IRC software, and the IRC services, youd then need to compile, and configure them. This is very unadvisable by me unless you have a somewhat advanced knowledge of IRC, and be able to find your way around Unix (that is if the software you're using is going to run on Unix, which personally to me is the only way to do it, although you can use Windows, which i strongly disadvise).
