To be trusted you must be trustworthy. You must also be visible. If no one knows about you, no trust will be invested in you. With those close to you, such as your teammates, this should not be an issue. You establish trust by being responsive and informative to those outside your department or team. Occasionally, someone will abuse this trust and ask for unreasonable favours. Don't be afraid of this, just explain what you would have to give up doing to perform the favour.