“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.”
—Richard P. Feynman

Science is a logical method used to help understand the natural world. Unlike deductive logic which leads directly to factual conclusions, science employs the "fuzzier" logic of induction or abduction to support explanations with observations. Inductive logic

One of the most effective ways to think critically is to employ the scientific method.

Steps of the Scientific Method

1. Identify the problem.
2. Gather data related to the problem.
3. Come up with an explanation (hypothesis) that accounts for all the data related to the problem.
4. Test the hypothesis by performing experiments or by gathering more data.
5. If the new observations agree with the explanation you have a stronger hypothesis. If the new observations do not agree with the explanation, you must either fix the hypothesis to make it agree with the observations or come up with a new hypothesis that accounts for all the data.

For example. Suppose a building inexplicably falls down. You want to find the best explanation for why this happened. You notice that this building was on fire and was damaged by another building that fell down. Based on the available evidence you conclude that the most likely explanation is that the building was weakened by debris and fire which cause it to collapse.

You continue to perform analyses and experiments on the building discovering new facts that the debris and fires did not cause enough damage to weaken the building. You also found that the building was in free fall for several stories. These new facts cannot accounted for with your first explanation so you throw out the old hypothesis and now favor the hypothesis that the building was a controlled demolition since this is the only available explanation that accounts for all the known data.

Falsification

When new observations are at odds with a hypothesis, these observations falsify or prove false the hypothesis. This extremely important process is called falsification. Every scientific explanation should be falsifiable. An explanation is falsifiable if there would be some way to prove the explanation false.

e.g.:

"There is a totally undetectable, invisible elephant in this room."

This claim is unfalsifiable because any attempt to disprove it (such as by showing there's nothing in the room) can be countered by the claim that the elephant is undetectable. In other words, no evidence could ever prove its non-existence.