You can view private Facebook profiles in one method, and one way only:
Getting a friend request accepted.
People talk about third-party apps that allow you to "hack" Facebook, but I can tell you for sure that these are just scams and people trying to make money off you (by asking you to pay for the app or take a survey etc...)
If you want to learn how to get a friend request approved without then you can read this: http://technology.blurtit.com/3976244/how-to-view-private-albums-on-facebook
You might be interested in taking another approach: Forget about viewing their private Facebook profile, how about HACKING THEIR PASSWORD and getting access to THEIR Facebook account itself!
If that's what you want to learn how to, watch this video called "How to Hack Facebook Passwords"