This thought provoking research piece by Edelman is well worth your time in placing brand trust in to a global context.
The survey has noted an increase in the value of peer-to-peer communication over the last few years. Clearly this is a bit scary for traditional marketers - journalists, celebrities & well-known on-line personalities are all in the bottom half in terms of their influence.
By contrast, friends & family, your employees, the CEO and your communications to customers are amongst the most trusted sources. These are all people who are either in the company or very near the company. In that sense it is should be 'easy' to influence them.
Firstly, by doing a good job and being nice to people. A bit of a given, one would hope.
Second, by communicating with these groups in a regular, helpful and non-annoying way.
2016 Edelman TRUST BAROMETER - Global Results