I don't know about WikiMedia, but most premade web software (PHPBB, Wordpress, TikiWiki) requires you to FTP a bunch of files onto your server and then activate the installation by going to a certain URL. You usually also to have MySQL support to do it.
UPDATE: I just read the installation instructions. OK, here's what you have to do:
1. Unzip the package into a direction on your computer
2. Create a subfolder on your webserver (such as /wiki) and copy
3. Through your FTP program, change the permissions for the config subfolder to 777.
4. Create a MySQL database. You should be able to do this through your account on your account on your webhosting service's site. If you are using a free site such as .tk, Geocities, or Tripod, you do not have MySQL support and you can't install it. Be sure to password protect the database when you create it. Be sure you know the database name, username and password, you will need them for installation.
5. Install MediaWiki by visiting
http://www.yourdomain.com/installdirectory if that doesn't work, visit
http://www.yourdomain.com/installdirectory/config. This will install the software.
6. After installation, copy LocalSettings.php from the config directory into the main directory. Delete the config directory.
You're done.