You can't simply drop mdf file in folder to make it available to SQL server. You first have to attach a mdf file.
You next have to make it available to SharePoint. The fastest way is to use the central administration or POwershell (if you are using SP 2010) to attach the DB. Here is a sample snippet :
# get the webapp that should serve the content
$webapp = get-spwebapplication http://yourserver
# attach the db
Mount-SPContentDatabase -Webapplication $webapp -name NameOfYourDB
This script assume the DB is attached in the default SQL Server instance of the farm.
Behind this point, the web application will be able to serve the document library.
A final note, you talked about a "corrupted" document library. This method will mount a full content database. If you want to restore only one library, you will have to execute these steps in a separate environment, then to export the desired content before reimporting it.
Some solution can do that out of the box.