Science is defined by the method scientists use to make discoveries and produce knowledge. The scientific method separates science from unsuccessful attempts to produce knowledge which people try to sell: faith, religion, pseudoscience, etc. Understanding science means understanding how the scientific method works, how scientists work, and so why science is superior to the alternatives. We rely too much on science to pretend it's no better than or different from the alternatives.
The scientific method is a combination of induction and deduction feeding back upon the other. Induction is taking information from our senses and producing general statements about our world. For example, we observe that fire consistently burns our fingers and conclude that fire is too hot to touch. Deduction is taking a general principle about the world and deducing what will or should happen in particular instances. Thus working from the principle that fire is too hot to touch, we deduce that putting a foot in fire causes burns and pain.
Because the scientific method is a feedback loop of induction and deduction, it often isn't possible to determine where the process has started, but a common starting point is used here:
We observe something about the world and arrive at new knowledge. This information might be obtained through any or all of our senses; it may come through intentional efforts or accidentally.
A single observation has little long-term value, so more observations are necessary. New observations are obtained deliberately as part of an effort to confirm or refute the initial observation in #1. Observations can be stated in the form of a question or problem, for example: In situation S, does X always occur?
After arranging and considering our observations, we create a general principle to describes what happened and, more importantly, explains why it happened. This principle, called a hypothesis, should be framed as broadly as possible: In situation S, X always occurs.
To see if our hypothesis is correct, we need to create deductions phrased as predications in the form "if principle P is true, then X should occur or fact F should be true."
Once we have predictions, we need to collect more observations by testing them. We need to determine if some fact (F) is already true or if some event (E) occurs or can be caused to occur.
6. Induction (again):
After we produce more observations, we need to look at our general principle again. If our predictions were true, our hypothesis is stronger; if this is successfully repeated multiple times, the hypothesis may be called a 'scientific theory.' If our predications failed, there are three possibilities: our theory was mistaken and we need to reformulate it; our deductions from the theory were mistaken and we need reconsider our understanding of it; or our experiments were flawed and we need to try again. Notice that this involves going through the scientific method again on a different level.
It can be tough to say where in the feedback loop of the scientific method one originally started, but the order of the steps is important. You can't hypothesize before observing and stating a problem and you can't test a hypothesis unless you have a hypothesis to test.
This is also an iterative process: testing provides new information even if the hypothesis fails. Sometimes you may go back to observation if you discover that stating a clear solution to the problem is difficult. Thus it is possible to move backward through the process as well as forward. Moreover, the process can be hierarchical: each stage of the process may involve using the scientific method to solve sub-problems or related problems.
The above is far easier than it may sound. The scientific method is only a formalized description of what people do every day. Even when described technically, the scientific method is just systematized common sense. Tim M. Berra explains how and why in his book Evolution and the Myth of Creationism. First will be the simple description and second will be the formal description:
1. You walk into a room in your house and flick on the light switch, but nothing happens. You flick it a few more times to make sure it isn't working and then go get a replacement bulb. After you put it in, you find that it still doesn't work. Looking around at the other electrical appliances in the room, you don't see any of them working either, so you go down to the basement to check the fuse box.
2. You walk into a room in your house and flick on the light switch, but nothing happens. At this point, you have an observation: the light isn't coming on. Immediately you form a hypothesis: the connection isn't making proper contact. You predict that, if this hypothesis is true, then it may be possible that it will make a connection with further attempts, so you try the switch again several times.
Unfortunately, your experiment does not produce the results you hoped for, thus your prediction fails. Your experiment was valid and your understanding of the principle is probably valid, so you have to go all of the way back to the beginning to try a new hypothesis: the bulb is burned out. If that is true, then replacing the old bulb with a new one should produce light, so you go to fetch a new bulb.
Once again, your experiment fails; once again, your experiment and your understanding of your hypothesis were probably valid, so you need yet another theory. Looking around, you make the new observation that nothing else in the room is working, so you theorize that the power to the room must be interrupted. You also predict that, if this is true, you will find evidence of that in the fuse box, so you go down to the basement to check.
These are two descriptions of the same events, but the latter is just a lot more explicit and detailed about thoughts and procedures that usually go unsaid — and that we're often unconscious of. The scientific method is so formalized and explicit because it is important that nothing be missed accidentally, and second, it is important that others be able to replicate our steps to determine whether or not our results are valid.