For several decades, there has been an organized campaign intended to produce distrust in science, funded by those whose interests are threatened by the findings of modern science. In response, scientists have tended to stress the success of science. After all, scientists have been right about most things, from the structure of the universe to the relativity of time and space.
Stressing successes isn't wrong, but for many people it's not persuasive. An alternative answer to the question "Why trust science?" is that scientists use the so-called scientific method. But what is called the scientific method isn't what scientists actually do. Science is dynamic: new methods get invented; old ones get abandoned; and at any particular point, scientists can be found doing many different things. False theories sometimes lead to true results, so even if an experiment works, it doesn't prove that the theory it was designed to test is true.
If there is no specific scientific method, then what is the basis for trust in science? The answer is the methods by which those claims are evaluated. A scientific claim is never accepted as true until it has gone through a long process of examination by fellow scientists. Scientists draft the initial version of a paper and then send it to colleagues for suggestions. Until this point, scientific feedback is typically fairly friendly. But the next step is different: the revised paper is submitted to a scientific journal, where things get a whole lot tougher. Editors deliberately send scientific papers to people who are not friends or colleagues of the authors, and the job of the reviewer is to find errors or other faults. We call this process "peer review" because the reviewers are scientific peers—experts in the same field—but they act in the role of a superior who has both the right and the responsibility to find fault. It is only after the reviewers and the editor are satisfied that any problems have been fixed that the paper will be printed in the journal and enters the body of "science."
Some people argue that we should not trust science because scientists are "always changing their minds." While examples of truly settled science being overturned are far fewer than is sometimes claimed, they do exist. But the beauty of this scientific process is that science produces both creativity and stability. New observations, ideas, explanations and attempts to combine competing claims introduce creativity; transformative questioning leads to collective decisions and the stability of scientific knowledge.Scientists do change their minds in the face of new evidence, but this is a strength of science, not a weakness.