US citizens have very little power over the judicial branch of the federal government. What power they do have is exercised only indirectly.
The judicial branch is, on the federal level, completely unelected. People have no chance to vote for or against any judges. This means that they cannot exercise any sort of direct control over the judges.
However, people can exert indirect control over members of the judicial branch. The people have to do this through their elected representatives. For example, the people vote for the President, and the President nominates judges. In addition, the people vote for Senators. Senators have the right to reject the President’s nominees. Senators are also typically given at least some informal control over the appointment of federal judges in their states. In this way, regular citizens can at least have some amount of power because they can vote for the people who decide who the judges will be.