There are 2 Ways to Successfully Unlock Songs
In Game Mode, successfully clearing 2 songs on at least "Difficult" will lead to a "bonus" song.
This song only allows you to make 4 mistakes, and plays quicker than normal.
The 2nd way, is through Quest Mode.
Completing a Club challenge will usually net you a new song unless you have already unlocked it through some other means.
Hope this helps!