The MediaMonkey database and most settings are stored as described at:
http://www.mediamonkey.com/support/index.php?/Knowledgebase/Article/View/16

To backup the library, you should back up the database file whenever you backup other files on your system to ensure that hard disc failure will not result in any data loss.

If your computer or drive has been trashed, you can recover your database as follows:
1. Install a copy of MediaMonkey to the new hard drive or PC. Don't bother scanning a drive and building up a database.
2. When MediaMonkey isn't running, copy your backup database to the default database location

At this point, your database will be recovered, however, if the music has been moved to a different drive or location, it will all be greyed out.
To correct this, see:
http://www.mediamonkey.com/support/index.php?/Knowledgebase/Article/View/92