The installation of most extensions in MediaWiki consists of downloading the extension's archive and extracting it in the extensions/ folder within your MediaWiki installation. For the purpose of this tutorial we would use the Score extension.
After uploading the extension and extracting it in extensions/, you can enable it simply adding the wfLoadExtension( 'ExtensionName' ) line in the bottom of the LocalSettings.php file, e.g.:
wfLoadExtension( 'Score' );
Generally, each extension should have a Readme file that will explain if it needs any special actions taken before the installation.
For this one a few other lines should be added and configured in the LocalSettings.php file:
$wgScoreLilyPond = '/path/to/your/lilypond/executable'; /* required */
$wgScoreAbc2Ly = '/path/to/your/abc2ly/executable'; /* if you want ABC to LilyPond conversion */
$wgScoreTimidity = '/path/to/your/timidity/executable'; /* if you want MIDI to Vorbis conversion */
$wgScoreTrim = true; /* Set to false if you don't want score trimming */
And the directory lilypond/ should be created in this case.
That's it! Your extension is successfully installed now.