1. Download the latest version as a compressed file from the
MediaWiki website (Wikimedia is an NPO, or non-profit organisation)
2. Upload the file to your public_html directory. The cPanel File Manager has an upload function, but I prefer to use an FTP client.
3. Extract the files and folders.
4. You'll now need to create a MySQL database. In cPanel select "MySQL databases" and follow the instructions to create the DB. You can name it whatever you want, but make sure to remember the name.
5. Next, follow the instructions to create a MySQL user. Make sure to remember the username and password. Once created, there should be an option to add the user to your wiki's database. Select it and give the user ONLY the following permissions:
create
select
insert
update
delete
alter
lock tables
6. In your web browser, navigate to the wiki directory of your site (if you installed MediaWiki into a folder named "wiki" in public_html, on a site name "example.x10hosting.com", the path will be "example.x10hosting.com/wiki").
7. There should be a link to the installation script. Click it and follow the instructions to set up your wiki.
8. Once the wiki has been installed successfully, go to your wiki directory and delete the folder named "config".
Note that you can expect to be following these same steps for nearly every kind of site software out there.
Once you've installed MediaWiki, you may want to look at the MW web site for extensions and ways to rewrite the URL to look like "/wiki/Page_Title" using a .htaccess file.