Bill Bishop, who made us aware that a "Big Sort" had turned America into islands of like-minded people, has a discouraging piece in the Post detailing the enormous loss of trust in most institutions, except for the military. It has happened mainly since the 1970s [hello, Vietnam! hello, Watergate!].
While there have probably been multiple causes including individual self-absoprtion and a decline in community engagement, Bishop offers no remedies to restore trust.
I don't have any far-reaching ideas to offer either. Congress and the presidency can help their own situation by getting things done -- and that means centrist compromises. The news media are too numerous and fractured to save themselves as a group, but individual organizations can triumph through professionalism rather than partisanship. The counter example of the U.S. military offers a potential model -- of accomplishment, professionalism, nonpartisanship [mostly, so far], and built-in self-criticism mechanisms.
Trust can't be demanded; it has t be earned.