Trust is a tricky thing. Only when you have an opportunity to break trust do people really start to trust you. When something goes wrong and you step up and accept responsibility, you will gain greater respect and build a valid reputation, which in turn will allow people to feel more apt to do business with you.
Now you don't want to go around creating bad situations just so you can show how trustworthy you are, but when a situation arises...
Honesty is the best policy
A few nights ago my oldest daughter (5 years old) got out of bed after lights out. In our house this has its repercussions (a stuffed animal gets put in time out). When I asked her if she had gotten out of bed, she looked at me with wide eyes, and said "Yes." She looked at me in silence as she waited for her punishment.
How could I punish such innocent honesty. I thanked her for being honest and told her that because she told the truth, I would not put an animal in time out. Her face beamed with joy and she quickly fell asleep.
It would be great if we never made a mistake and conducted business perfectly every time. There may be times when you are called into question and the best way to deal with any questions, no matter what the cost, is to be honest. You may have to deal with consequences, but people will trust and respect you even more.
Respect others and let them know you trust them.
This is not to say believe blindly everything that you are told. But when people are given the benefit of the doubt, they tend to be more loyal. This can be accomplished in many ways. Asking simple and small favors shows that you have faith and trust that he/she can and will follow through. Any type of responsibility given to someone creates a bond of trust, not only between you and that person, but others who observe the interaction. You are a trusting person, who is worthy of other people's trust as well.
What are some ways to demonstrate that you trust other people?