Well you can install most PHP and Perl based wikis on your Mac. You just have to know how to a) enable PHP/Perl on your Mac, b) enable the web server and c) install the actual wiki software. Depending on your skill level, it may be tricky to get that all setup.
you would set it up just like any other server, just don't have any of the outside requests for webtraffic routed to your machine (don't touch the router) and then all the people on your local lan will be able to access your machine and no one from the outside.
My suggestion is to use mediawiki. I set that up on a Linux box and it only took me an hour or so to get started.
Most of the components are already installed on macs(Apache and php) and you can just search google for mediawiki, there are plenty of OS X installations out there. You will need a database(my suggestion is mysql), but that is probably the trickiest part. The defaults work great.