Hillary Clinton has proven to the American people that she cannot be trusted with the highest office in our land. Although the FBI didn't press charges, they said over and over how irresponsible she was with classified information, which potentially put our entire country at risk. She has no chance of winning back trust.
There were no "smoking gun" revelations from the Clinton email issue, and she has the opportunity to put forth a positive message at the upcoming Democratic National Convention. Meanwhile, Trump continues to face fraud lawsuits and allegations. Over the course of the campaign, Clinton will prove herself to be the more trustworthy candidate.
It will be very difficult, but Hillary Clinton can gain back what trust show had. She needs to be transparent in her actions from here on out, and be clear and concise in her communications. She cannot continue to hide behind walls of secrets and cover-ups to cover up cover-ups.
If you support Hillary Clinton, you are likely to keep on doing the same. If you don't, there's not a lot she can do. Read news articles and you'll find almost as many finding her trustworthy as those which do not. One journalist wrote that she looked extensively for some basis for the dishonest liar label, and although she is not a Hillary supporter, she didn't find anything based in fact. At this point, people have already made up their minds about Clinton.