There are at least two ways to do it.  One way is to make the software that
maintains the IRC channel log everything.  Another way is to write an automated
client ("bot") that stays logged into the channel pretty much all the time and
logs whatever it sees.  The former way is theoretically more reliable, in terms
of ensuring nothing is ever missing from the logs, but the latter way is
probably more convenient; the bot also can be given additional features, e.g.,
uses can send it private commands and get back answers (such as, the last n
lines in the log, for instance).

For the latter approach, one possible place to look for getting started is at
Net::IRC, here:
http://search.cpan.org/author/JMUHLICH/Net-IRC-0.75/IRC.pm
This is not a module I have ever used, though, so I don't know a lot about it. 
Frankly, I've not done much with IRC at all, even as a user.

The other thing is that the site really doesn't need IMO a complete overhaul. It
would be quite simple to simplify things by moving the right sidebar, replacing
the google search with the keyword search at the top of the screen, and then
tweaking the fonts, etc to focus more on getting to the clip art.

My primary interest in the site is two fold:

1.) Get Clip Art
2.) Submit Clip Art

Those are the primary interests IMO to anyone who visits the site.

(In reply to comment #2)

Think you commented on the wrong bug mate! ;)

Ooops...ignore my comment...wrong bug.

I don't think logging the IRC channel is worth the effort.
We've got limited manpower and a lot to do, and there's
not much discussion of interest on IRC worth logging.  ;-)