That trust is not built overnight but takes time to develop. Depending on your personality, you'll either start with trusting others until proven wrong or mistrusting of others until proven wrong. It's okay. It's normal.
Whichever way you start out, though, the trust is built in the studio in rehearsal time. How can you make people trust you? Well, you need to show up to rehearsals, participate in them, learn what you need to learn, you probably will need to practice on your own too, and just simply be there when you need to be there.
So, for a choreographed piece, if you're the choreographer, you trust that your fellow dancers will learn the choreography and practice it so that the group looks polished and delivers on the choreography's promise. If you're a participant, you trust your choreographer that he/she will do a good job interpreting the music and putting together a cohesive piece that will make the group look good. If it's a choreography built by the group, then you need to trust each other to do all that: learn what needs to be learned, practice, interpret the music correctly, etc. You will also need to trust each other in a group-built choreography that each member can speak his/her mind freely and a healthy discussion can be had about ideas.
When it comes to ATS/ITS, again, there's a whole lotta trust there! As the leader, you trust that the followers will understand your cues. As the followers, you need to trust that your leader will cue the movements correctly. And that's why we drill, right? To get those cues in your body memory.
Note also that whatever I said that you trust the other person to do is what that person needs to deliver. For the trust to be built, you need to deliver on what people trust you to do. ;) And there's nothing like glitches to prove how it's actually going to work.
So, Saturday, one member of our group ended up having a brain fart... but we followed. The ending of the piece didn't go exactly as planned (natural pitfall of dancing to live music) but I made them shimmy the hell out of their bodies and they followed. I didn't even have to turn around to know that they were following. I felt it. Granted, us three who were performing that day have been dancing together for 7 years now so we're VERY familiar with each other. But the point is that, even though we were totally off ITS script, we still were able to deliver a cool performance... because we trusted each other.
When you see a troupe that has great chemistry, the #1 ingredient is trust... even beyond friendship and just liking each other. We've all had friends that we love to pieces but, damn, they're always late, never do what they promised, etc. We still love them, but the trust is not fully there. So the same thing can happen in a group. I dare say that a good chunk of group drama is about this trust issue... and, well, crystal clear communication (but that would be a topic for a whole different blog entry). So, just like I mentioned in my Be A Good Belly Dance Citizen entry (see http://celestesmusings.blogspot.com/2011/08/be-good-belly-dance-citizen.html), you need to do what you said you would to build your trust with your group. And then you have fun moments like shimmying for ever while on stage and get to laugh about it. ;)