By far one of my favorite authors, Hemingway unknowingly gives a valuable lesson on management. He doesn't waste time with team-building exercises, or that initial "getting to know you" period. He goes head-on and instructs you to just do it.
It can be difficult to give up control, refrain from giving unsolicited advice, or (don't say it, don't say it, don't say it) admit that other people can do things better than you can - but you just have to do it. When the people around you are empowered with trust, they typically will honor that trust and overachieve (if they don't, then it's time to sit down and have a conversation). On the flip side, when you empower others with trust, you naturally begin to feel more connected to them. Sounds like a pretty nice work environment to me!
There are a couple ways that the trust stuff can unfold in the workplace, especially when it comes to non-profits: office hour policies, vacation vs. work from home, non-micromanagement, higher levels of delegation, access to money, not having to be at every single event that takes place.
Give it a try, it's really great to see how people respond to freedom. It's also freeing for yourself.