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What Science Is
Science is a system existing for the sole purpose of understanding, to the best of our abilities, the natural world that we observe. Anything that is impossible to test, demonstrate, or explain rationally cannot be scientific, simply because science isn't about those things.

The proper use of science requires that we accept the following rules:
1 The truth is not relativistic. It does not change between places, times, or cultures.
2 The three laws of thought are universally applicable. One of A and ¬A must be true, the other must be false, and A can never be ¬A.
3 Any unique real event must have a unique set of real reasons for its occurrence, all of which must be true. It cannot happen for unrelated reasons or no reason at all.
4 All data obtained from observations must correspond to some real thing. They cannot be completely meaningless.
5 Everything that exists in reality must comply with the first four rules.

What Science Is Not
Science is not dynamic; it does not do or say anything. It is completely impartial in all things, even when scientists aren't. Science cannot be a means of solving everything, nor can it be used to prove or disprove anything. If anyone says that science proves, claims, denies, or lies about some fact, please correct them, because it does not.

Science also is not empirical; no amount of data is itself scientific. Science is only involved in the way that we obtain and interpret our data. If repeating an experiment produces wildly different results, something in the experimental setup has changed and must be identified. If different experiments reach incompatible conclusions, one of the conclusions is wrong. The data itself does not change that.

Scientific Method

Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.

Ibn al-Haytham

The underlying process of science is the scientific method. This is a cyclical process similar to the tensile testing of alloys: Valid ideas are separated from invalid ones by increasing the requirements until something (either the idea or the requirement) breaks. When that happens, the weak points are replaced and the process starts over. The key steps in the scientific method are described below:

Research: The first part of any investigation should be figuring out what you are going to investigate and whether it has been investigated before.

Hypothesis: This is the idea that you're starting out with. The purpose of stating a hypothesis is to indicate what it is you are examining to see if it's related to something else. It is not comparable or even related to a scientific theory.

-A sneeze is a rush of air through the nasal passages is a bad hypothesis because it doesn't tell us anything we couldn't find in a dictionary.
-People sneeze when they collide with the intangible souls of deceased humans is also a bad hypothesis because it asserts something that cannot be tested, demonstrated, or explained rationally.
-Sneezing is directly correlated to the incidence of colon cancer is a good hypothesis because it asserts something that is not already known about observable phenomena.

PLEASE NOTE: By no means should you ever attempt to prove a hypothesis. It is just a statement that is either true or false. As far as your investigation is concerned, using the null hypothesis (that there is no effect or relationship) is equally valid and, in fact, usually preferred by researchers.

Investigation: Experiments are performed to test the hypothesis based on what we would expect to happen if it was true or false. Ideally, these will be the only conclusions permitted by the experiment; if this is not possible, one or more alternative hypotheses must be introduced and tested as well. Any conclusion which complies with all experimental results may be incorporated into an explanatory model.

Suppose we start with the hypothesis that sugar is involved in one or more metabolic pathways. Our null hypothesis would be sugar is not involved in any metabolic pathways. We need to devise an experimental setup which will give different results if one or the other is correct.
A good experiment should be performed under controlled settings with multiple data sets for each observation, so that any significant differences in our observations can be attributed to what we're testing, rather than something unknown.
If our data is good enough to reach a definitive conclusion, we can present it to the scientific community so that anyone interested in the topic can repeat our experiment or build on it by examining the effects of different variables. Scientists will treat these as a track record for our conlusion, and will reject it if it conflicts with reality.

Model: If several verified conclusions appear to be related, we can sometimes combine them into a more general set of rules called an explanatory model, which is used to explain how something might work in any conceivable situation. A model is tested by seeing if it matches up with all of the things we already know (the minimum requirement for any successful model) and then seeing if it's compatible with existing theories that we have already tested thoroughly. A model that survives these tests may one day go on to become a scientific theory, which is basically the greatest aspiration a model can have.

PLEASE NOTE: It is quite common in newer fields of study to have multiple different theories that all explain the same thing in different ways. This happens because they all fit the same facts equally well, so we can't discard any of them until we have done enough research to rule out the invalid ones.

Pseudoscience

Yet scientists are required to back up their claims not with private feelings but with publicly checkable evidence. Their experiments must have rigorous controls to eliminate spurious effects. And statistical analysis eliminates the suspicion (or at least measures the likelihood) that the apparent effect might have happened by chance alone [...]

Richard Dawkins

Pseudoscience is a way of padding a speech, article, or report with sciencey-looking content that is meant to give the illusion of well-supported fact. This makes it easier for fraudulent or faith-based claims to gain the trust of the general public without submitting to the rigorous testing of the scientific method. Public belief in pseudoscience is harmful to the scientific community, as it allows patently false ideas to propagate and gain general acceptance, it promotes the use of poor research and flawed argumentation, and it injures the public image of scientists in general.

How To Detect Pseudoscience:
-If the subject matter is inherently unscientific (anything that can't be tested, demonstrated or explained rationally), it cannot ever be science.
-If it lacks any logical connection between observations and conclusions, it cannot ever be science.
-If it uses anecdotal accounts or subjective interpretation to arrive at a conclusion, it cannot ever be science.
-If it considers the main hypothesis to already be proven (circular reasoning), or considers only one of several possibilities (causal oversimplification), it is not good enough to be science.
-If the authors leave out crucial details needed for independent verification, or refuse to make any definitive tests, it is not good enough to be science.
-If it cites dubious reiterations of its own claims (false authority), or references other works for information that is not contained within those works (misattribution), it is not good enough to be science.
-If it bases general conclusions on very limited data sets (hasty generalization), omits data without explaining why (cherry picking), or treats a statistically meaningless data cluster as an undeniable correlation (texas sharpshooter fallacy), it is not good enough to be science.

PLEASE NOTE: When I state that something is "not good enough", I do not mean that the conclusions it draws must be false; only that it cannot support them.

Other Things Of Note
Scientific Law: This is a mathematical formula that shows the relationship between two or more variables. It is demonstrated by consistent empirical observations. Laws are often incorporated into theories that further explain the relationships.

Proof: This is the absolute confirmation of the truth of something. Proof can only be achieved using mathematical logic; no amount of consensus, belief, or observation will ever result in proof.