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.
Fig 1: The Scientific Process
The goal of the process is to create a new theory or investigate an existing theory.
We start by observing things in the world around us, then asking questions about how these things came to be that way.
A hypothesis is then proposed that might answer the question. 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, it gains credibility. The hypothesis will then usually be subjected to more experiments and observations in an effort to increase its credibility further.
Experimental results which contradict the hypothesis will naturally cast doubt on its 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 hypothesis 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 and may become part of a new theory.
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.