IJ Reilly said:
Should my domain host be handling the install anyway?
Depends whether you've contracted with somebody to build and run your site, in which case yes, or whether you just have a webhost to which you upload files, in which case no.
Dreamhost (a decent mid-sized webhost) has an auto-install for a basic Wiki if you don't have any fancy requirements, and there's at least a small chance your webhost has some "standard" software packages that they'll automatically install for you (or more likely you can automatically install for yourself using their control panel).
If you're not that lucky and you're not comfortable installing server-side software yourself (it's really not that hard if you follow the instructions carefully, but it can be VERY scary), your only option is to pay somebody to do it. Shouldn't cost a fortune, anyway.
If it's a very small project, you might check out TiddlyWiki:
http://www.tiddlywiki.com/
It's a weird Javascript-based Wiki that essentially uses a mess of in-browser scripting to let you save a single HTML file to your hard drive and use your browser to edit its content as if it were a full-on Wiki. Once it's set up, you can save it and upload it, and it'll work (but not be directly editable) on the web. Runs surprisingly and is fun to mess around with, though I'm not sure if it's the right tool for your needs--generally it's better for setting up single-person Wiki-style sites.