Although there are websites out there that claim to teach you how to view a private Facebook profile, there isn't really a safe or legal way to do it.
Facebook is one of the biggest websites in the world, and they take a lot of time to protect their user's from people who want to view their private information.
The importance of privacy
Most people set their Facebook profile's to private so strangers can't snoop around their images and statuses. There is obvious logic in this approach, and therefore it's pretty immoral to try to view this information against someone's will.
I'd advise that you simply send the private account a friend request and see whether they actually want to engage with you. If not, no big deal, but don't bother trying to hack into it. You'll likely fail. Even if you succeed, you'll likely find yourself in some trouble.