You can create a favicon manually on your computer or you can use an online favicon generator. Here are several such generators:

Dynamic Drive Generator

Graphics Guru Generator

1Favicon Generator

Once you create the favicon, you should upload it to your MediaWiki folder. Then in LocalSettings.php you should add the following line:

$wgFavicon = "$wgScriptPath/favicon.ico";

Clear your MediaWiki page cache to see your new favicon :)