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Over time, the most effective way to build trust with another individual is through honesty. Demonstrate consistently that you will do what you say. Not lying is easy. But it is even more important to be conscious of not shading or masking the truth, and even being careful to avoid omitting important details. Any of these behaviors, no matter how innocent, can create doubt in your credibility.
When a person who doesn't know you first meets you, it isn't necessarily your public facing personality that formulates their perception of you. They're judgment of your trustworthiness will initially be based on the confidence in your greeting. Making and maintaining eye contact is absolutely essential from the beginning. Success in this initial phase will determine whether the person is even open to learning your true underlying character.