First, the players need to trust me. They need to understand that I am going to work to the best of my abilities to gain the knowledge to help them be successful. In today's world it must be visible. They must see that I am going to clinics, working on practice, scouting games, and having good game plans. They may not realize it, but they trust that the coaches know what they are doing and trying to help them be successful.
Players will hear negative comments about the coaching staff around friends, girlfriends, family members and it makes it that much more important that they can trust you. You must make that trust be something that transcends the court. Can your players trust you to have their backs at school, academically, issues that happen in the community and if need be economically. "Having their back" doesn't necessarily mean you are getting them out of trouble or complaining to teachers about players grades. What it does mean is allowing for time to work on school work and possibly discipline for off the court issues. That trust is between you and the player involved, but the rest of the team as well. Are you consistent? Are you letting some things slide?
A coach must be able to trust the players also. My rules are set up to ensure trust, but hopefully to teach my players the self-discipline to be trustworthy. I have had people ask me why is having a haircut or some of my other rules important. I have answered that I need to know that when I say "shave" they will do it, or better yet I don't have to tell them at all. Because I believe there is a direct correlation in a player who will "shave" when I say so and who will also run the play I tell them with ten seconds to go in a game. I/We need to have that trust in each other.
In a high school situation, trust is important and the players are going to test and sometimes lose your trust. They should never (as well as their parents) have to worry about trusting you as a coach. We all are going to make mistakes, but there needs to be some trust that the players and their parents know you are going to set a good example, and will be around to coach the team an entire season. Breaking laws or being unethical is something that shouldn't enter into the equation at all, but seems to do so more and more each year.
Trust is important in a team. Any team. It doesn't matter if it is a basketball team, a teaching staff or your family. Trust is a building block of success.