The steps are:
- Ensure PHP, MySQL, and other pre-requisites are installed.
- Then decompress the source into a directory, which is either in webroot or is symbolically linked there (my personal favourite).
- If you're finicky, you'd like to create the MySQL user and database before installing, otherwise just leave it to MediaWiki.
- Open the form for configuration and installation, fill in the required details, and you're up and running! Oh, you can accomplish step 3 here by just specifying the username and database name you want to create along with the MySQL root account's password.