Trust - hard to build, easy to break, and critical to good decisions. Creating it in your team has the same factors, and then some because so much of building trust is modeling the right kind of behavior.
This article is rich with advice on how to create and maintain trust in your team. It starts with the leader, developing the trust in yourself and then extending that to the team.
In the end, for you to trust your team, they have to trust you, and that starts with demonstrated that you can be trusted. Seems circular, but it is a cycle that you have to create and then reinforce.
To create work environments in which trust can flourish, we first need to understand how it really works: the various ways it can be given, built, and broken. Once we do, we can teach ourselves how to act (and react) in ways that help it grow, even in the most challenging situations.