The scientific method is a procedure, shown in the flow-chart below. It may seem long-winded but the point is to keep it consistent. And that's the most important concept to understand -- this process is consistent. If I propose a theory and support it using this method, you will also be able to test it using the same method. You don't have to blindly trust me, you can see for yourself if my theory is valid.
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Fig 1: The Scientific Process
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The process begins with a theory. There are many ways in which a theory can be developed.
A hypothesis is then proposed based on the theory. It must meet certain conditions.
Experiments and observations are then conducted which attempt to either support the hypothesis, or disprove it. If the experimental results support the hypothesis, the theory gains credibility. The hypothesis will then usually be subjected to more experiments and observations in an effort to increase it's credibility further.
Experimental results which contradict the hypothesis will naturally cast doubt on the theory's credibility. At this stage, more experiments (or different ones) may be performed in an attempt to gain support. If the results are consistently unfavourable, the theory must either be modified to explain the results, or abandoned altogether. Note that modifying the hypothesis is valid, not cheating (e.g. Galileo's gravity).
If a hypothesis gains continuing experimental support without contradictory evidence, it will tend to become accepted as valid. Note that experiments do not generally prove a hypothesis to be correct, they only support it's validity. (In contrast, a hypothesis can be disproven by experiment.) This is a good principle to use - it helps keep our arrogance in check.
It's quite possible that a hypothesis will go through many stages of experimentation - sometimes gaining support, sometimes losing it. Eventually, the evidence will usually stack up on one side. If the conclusion is false, but the argument is valid, then the hypothesis must be false.
It's clear that the scientific method is often not a black and white affair. Whilst many theories are easily proven or disproven, many more are not. Many theories are argued over for years.