Out the top of my head, things you should keep in mind:
- It's a relationship like any other, and you earn each other trust through your interactions over time. So you need to be extremely reliable and responsive if you want to be perceived as trust worthy;
- If something bad happened, be transparent and the sooner you say it the better. It's extremely uncomfortable, and you'll try to delay it because you don't want to say shit happened, even if it wasn't your fault.
- Never bring up a problem without a solution, or a potential solution, or a recommendation for a solution. No one wants problems, we all have plenty of those. Even if it's something out of your control, you should always spin a solution for it.
- Always reply, never leave someone hanging;
But you'll only get these things rooted by exposing yourself and doing it. You'll just be missing someone to course correct you, and nudge you in the right direction.