In a nutshell, the scientific method works as follows:
1. Start by observing something, collecting evidence or facts.
2. Think of a way to explain what you've observed. Use your explanation to try to predict something you haven't observed yet.
3. Test your explanation by trying to see if the prediction is correct or not.
4. Revise your explanation based on the test results.
This works because:
a. It's based on repeatable observable facts, not wistful thinking.
b. It's fully transparent: anyone can repeat the process to confirm or deny another person's claims.
c. It's self-correcting. If mistakes are made, deliberate or otherwise, they will eventually be found and fixed.
d. It's an accumalitive process. Knowledge gained by older explanations is used to make new observations and test our understanding of them.
For a more technical explanation, you might want to read this:
http://en.wikipedia.org/wiki/Portal:Scientific_method