Trust me!

So recently someone was asking me about how to develop trust within a team.
Trust in teams and organizations: its pretty much a perennial concern. Everyone wants trust. Let's face it; everyone wants to be trusted, everyone wants to work with people that they trust, we know that trust has some positives associated with it (e.g. reduced conflict, increased information sharing, etc.) and has relatively few downsides.
But in our 24/7 instant-on-demand culture, we want trust to develop faster. We want to develop trust before the team starts, we develop team-building sessions to help create trust, we find ways to encourage (or even force!) non-task social interaction in order to develop trust. Especially in virtual teams, where team members do not have the opportunity to meet face-to-face, we are concerned with the impact on trust.
What we often forget is that trust is primarily an outcome of social/task processes, not an input. When you first meet someone you have neutral trust with them - or rather, you have whatever trust you happen to have in the social context. If there is a strong social system with distinct rules and laws, then you have trust in those rules & laws rather than trust in the individual. If you meet someone in a relatively lawless environment, then you are going to be suspicious of them until they have given you reason to trust them. So trust is an output first, and then becomes an input into social processes over time.
So, the best way to build trust within a team is let people start interacting and performing. Over time (and really, not that much time if they have the opportunity to work on shared tasks), they will get a very realistic sense of how much they can trust each others' motives, values, intentions, competencies, etc.
But still, some people will want to speed up the development of trust within their team. Sorry, you can't. You cannot force two people to trust each other. You can however build up a social system in which they can place trust, regardless of the trust they may have for each other (positive, negative or neutral). So what you do is focus on building very clear, shared goals for the team - working to make sure that everyone's motives and intentions are in alignment with each other. You create very clear roles for everyone on the team, and explain to all team members what John Doe brings to his role and what Jane Smith brings to her role. This helps to build trust in people's competence. Finally, you encourage communication between group members about their task, as it is hard to feel interpersonal trust for someone who is isolated from you. Now you have a system that encourages trust in the short term, plus the interaction to build interpersonal trust over time. So sit back and start enjoying the task, the trust will come.
Go on, give it a try!