There are times when you are handed over an .mdf file and are tasked to create a new database out of it.  There's no log just an .mdf file.  The easiest way to create a new database is to use the query editor in SQL Management Studio type the following into the Sql Query window

CREATE DATABASE Northwind
 ON (name= 'Northwind',
 filename = 'C:\Northwind.mdf')
FOR ATTACH_REBUILD_LOG;

The query above will create a new database for you call "Northwind", all you have to do is specify the location of the .mdf file and the "FOR ATTACH_REBUILD_LOG" will rebuild the log for you. You might run into a "Access denied" error but it's a permissions issue. Make sure the user that is running the query has permission to the file.