Well firstly you'd need a shell account or cable internet so the server is up full time.
I don't think running it on a 56k modem is ideal especially with most Internet Service Providers allow up to 2 hours of connection then need to reconnect plus it'd be as slow as a snail.

Other than that there is IRC server software all over the WWW.
Webmaster's conference room.
UnrealIRCD

Here is a good link for IRC server software.