The first is to be vulnerable with each other, ask stupid questions, and propose stupid ideas. Without this vulnerability, team members are reserved and will keep ideas and insightful questions to themselves. Many great ideas started with stupid ideas, and stupid questions. Without trust, you would not be willing to be vulnerable with the others, for fear that they would make fun of you or tell others.
The second is to feel comfortable enough to provide constructive feedback to others on the team. Without such feedback, bad ideas may go through. Team members would fail to see the flaws in their ideas. You will be forced to have "the meeting after the meeting," where the value of ideas would really be judged without the presence of those who suggested them, or their ability to defend them. Note that being comfortable providing constructive criticism is not a license to personally attack or ridicule the proposer. "Say what you mean, mean what you say, and don't be mean when you say it." Without trust, you would not offer criticism, because you would worry about how the recipient would take it, and the consequences.
Finally, the third is to feel confident enough to accept such constructive feedback. It is very easy and natural to become defensive when criticism is offered to you. But keep in mind that while maybe 10% of the feedback you are getting it true, 100% of it is true in perception. Is that the perception you want? Instead of being defensive, try to see the feedback for what it is--an attempt to improve your idea or answer your question. Without trust, you would not accept any of that feedback as true, as you would suspect ulterior motives drove it.
So trust is important. It takes time to develop, and there is a formula to understand it and accelerate it through turning and pulling the appropriate knobs and levers. But it will never, ever develop without the following three prerequisites.
1. Perceived Competence
You could never trust someone on the team who you don't believe is competent in what he or she does. Collaborative, high performance teamwork depends on every member doing their job, and doing it well. Not just the best they can. It requires that nobody's actions would need to be second-guessed. If a team member is incompetent (or not competent enough), or even only perceived to be such--trust will not develop.
2. Shared Values
Every person is driven by a set of core values. Some values could be objectively and universally bad, while others could be objectively and universally good. However, most values could simple be different among different members of the team, and so could the prioritization of those values. One member could put family above work, while another could put work above family. Could you argue with any of them? (actually, I bet you could...) None of them is right, and none of them is wrong. However, a mismatch in the values or their prioritization could prevent trust from developing.
3. Fairness and Equality
We are driven and affected, to a large extent, by fairness and equality. If one member of the team is higher ranking than the others, the team could still be productive, but if that higher-ranking member is exercising their rank to overrule or veto decisions made by others, trust will not develop in that team. If one member works very long hours while the other leaves the office at 5pm sharp--trust will not develop between those two. We are driven more by comparing ourselves to others than by absolute measures.
Missing any of those three prerequisites between any two team members would prevent trust from building in that team, or dramatically slow it down. Here is what you can do about it:
If I don't know what's bothering you in me--I can't fix it, and I can't explain myself. Communicate what bothers you in others, and listen to what bothers them in you. Then go to step 2.
Once you understand how others see you, and you can understand their perspective, do your best to change. Look at this as an opportunity for self-improvement. If you don't agree with the need to change, go to step 3.
3. Make hard decisions
If any of those prerequisites cannot be met, someone needs to leave this team. Even if that person is you. Having trust in the team is more important than forcing people into the team because of their technical skill, job description, availability, or management direction.