Do we just have to put our faith in the non-profit and hope that they are actually doing what they say?
If you are giving to big charities (because they match up with your values), they have tons of data on what they are doing with the money. They also sometimes have internal funds you can donate to that are earmarked to only be spent on a specific activity -- just ask.
I've volunteered and served on boards, too...a great opportunity to connect with your "community" and gain a deeper understanding of the issues affecting it...
Also, from a personal standpoint, I try to give in accordance with Peter Singer's recommendations that you should help the worst off first (So things like Malaria Nets and de-worming). It's easier to be sure you're making things better if the money goes to treating a life-threatening disease that can be prevented for a few dollars a head.
You can't really control how they use it. But you can see what they accomplished in the past. Look at what they are planning for the next few years. And then evaluate at the end of the year and see if you feel like they did what they said they would.
But, the non-profits I typically support function as "safety nets", providing niche goods or services that would otherwise be unavailable to their patrons...quite often those are quite basic--food, clothing, healthcare...