Trust must be earned. And you can earn it by always delivering on your promises.
When I tell someone that I will get back to her about some problem, I will get back to her to talk about the problem. When I promise to email a document, I will send that document. And when I tell someone that he has full responsibility for a job, I will refrain from interfering and mind my own business, until my input is explicitly requested.
We recently invited one of my spouse’s colleagues to stay for the weekend in our house in Brussels. At the morning of her arrival we were waiting for her call to tell us what time to pick her up from the railway station. But no call arrived. When we finally called her ourselves she said she wasn’t coming, for some vague and unconvincing reason. Any trust that I had in this person evaporated on the spot. Why someone would commit to a visit, and then not even bother calling it off, is beyond my understanding.
You build trust simply by doing what you have committed to. Trust means that people know they can rely on you. It is easy to build, but even easier to break. People destroy it when their behavior is unpredictably unpleasant. But trust also suffers when people are either predictably unpleasant (someone always doing precisely the things you don’t want him to do) or unpredictably pleasant (someone doing the things you want only when you least expect it).
Make sure that your behavior as a manager is predictably pleasant, and I’m sure you will have no trouble earning trust from your people.