1. Be reliable. Trust is not just about telling someone a secret and having them blab it, or something similar, part of trust in friendships is just knowing that if you need a shoulder to cry on, a ride when your car breaks down, etc. that your friend will be someone you can count on to be there for you. So, be reliable.
2. Be careful what you promise and commit to. While life happens, it is not excuse for being untrustworthy. So, part of being a trustworthy friends is knowing that life happens, and planning for the worst. Never say you will do something you can't. Never say you will be somewhere you won't. Then, if you do make that promise, have your plan for how it is going to happen, then a back up plan in case something goes wrong, or falls through, because in life it does. In other words, get a sitter, and have a backup plan. Have a car, and know someone you can call for a ride just in case, etc. A few slips will not damage the trust, but regularly committing to things and not following through is going to make you untrustworthy.
3. Listen and respect people. Part of being trustworthy is not repeating information that is private, embarrassing, etc. even if you did not say you wouldn't. In other words, be the kind of person that your friend knows they can share their deepest secrets, fears, etc. with, without worry that it will come out later, or be used against them at some point. Confidences shared are to be respected.
4. There is no other way to say that in order to be a trustworthy friend you have to exhibit trust than to simply say, be trustworthy. Do not lie. Do not tell secrets. Do not back stab, gossip, or do things that will hurt the person. Instead, hold their friendship dear, and be the kind of friend that deserves it and that they would choose to rely on because they know that they can.
5. Be kind. Part of being trustworthy is not using an intimacy as an excuse or convenient source for hurting someone. We often hurt the people closest to us the most because we can. So, if you want to be a trustworthy friend, you have to learn to become aware of people's insecurities, and never use them as ammunition, even when you are angry.
6. Be on time. It is a silly thing, but making plans with someone means extending your trust to them. It means expecting them to show up. So, if you want to show you are worthy of that trust, do not just show up, but be on time so that they never have to doubt you or themselves.
7. Extend trust. If you are always willing to hear other people's secrets, but never tell your own, it starts to feel one sided, and makes people feel like you can't be trusted. So, part of being a trustworthy friend is trading tit for tat.