If you're using SharePoint 2010, this is a textbook case for an unattached content database restore. Long story short, you need to do the following steps:
- Restore the database backup into your SQL 2008 instance
- Add the database as an unattached content database via a Granular Restore in the Central Admin site.
- Export the document library from the unattached content database
- Import the document library back into your site collection.
For more details on unattached content databases in SharePoint 2010, see http://technet.microsoft.com/en-us/library/hh269602.aspx
If you're using SharePoint 2007, you won't be able to take this approach. You're going to have to restore the database backup and either remove the original content database from your current farm or attach the restored backup to a completely separate farm, then export the document library. You cannot attach two instances of the same content database to a SharePoint 2007 farm.