I'd like to be able to make irc run from off a webpage like this http://www.black-cell.net/ircapp/ircapp.php

but don't know how to do it. can you tell me if there is a tutorial on how to do this or can you tell me yourself?

What you're looking for is a java applet. I'm not sure where you can get information about that. You might try googling for the information. If you were looking for a way to integrate mIRC, rather than just having an active IRC client, then, to the best of my knowledge, you are out of luck.

Please note that mIRC is a chat client that connects to IRC networks. It is not all of IRC.

you can put pjirc on your site and connect with mirc
http://www.pjirc.com
i have this on my website and it is great.
i have 2 mircs in my room .