Do you want to become trustful member (or a manager) of any project team?
1. Respond quickly: to the project team's emails, requests, calls. Even if you have to respond with "no" or "don't have time now". Just don't disappear.
2. Do what you've promised: Or find someone else who will. Or inform project manager that you will not perform. Just don't wait until the deadline and then search for excuses.
3. Show enthusiasm: and you will drag other team members out of almost any trouble that can occur within a project. Just don't be a dead fish and suck the energy out of the other team members.
4. Don't hide behind the others. Take responsibility for your part of the project. "It wasn't me" approach is bad for the project's morale.
5. Communicate issues early: if there is an "elephant in the room" (e.g. an issue nobody wants to address during a project meeting), raise your voice and address it. Better early, when the things can still be fixed. Everybody will appreciate it.
I'm participating in several international projects (for more than 15 years) and I can assure you if you ignore these 5 tips, you will make someone's life ... very unpleasant.