We all use science every day. It is simply rational thought, or to paraphrase Sherlock Holmes: when looking for a solution to a problem, we simply eliminate the impossible solutions, one by one, and whatever is left at the end is the answer. If you've got a set of keys and don't know which one fits the door, you go through them one by one until the door opens. You may skip keys that look like car keys, or keys that look too small or too large for the lock. You are thinking scientifically and solving the problem rationally.
Science is not some mysterious set of rules established and maintained by an elite set of scholars in an ivy-covered tower. It is the sum of the thought processes that allowed humans to survive thus far on Earth. We are curious creatures, born with no built-in knowledge of our environment, and everything we know must be learned. We are the descendants of beings who evolved with the ability to recognize connections between things and events in the environment (i.e., snakes with rattles should be avoided, white berries are probably poisonous, blue or black berries are probably edible, drinking salt water only makes you thirstier, etc...).
But this type of causal thinking is not infallible, and we sometimes make connections whether they exist or not. False negatives (i.e., snakes with rattles are OK, bears are friendly and cuddly, you can fly if you flap your arms fast enough) can get you killed, while false positives may simply waste time and energy (crossing your fingers will bring good luck, breaking a mirror will bring bad luck, stepping on a crack will cause catastrophic maternal spinal injury, etc...).
Our brains are thus designed to pick out patterns so we sometimes see patterns where they do not exist. Unplug the cable from your TV sometime (go ahead -- it won't affect program quality); stare at the static long enough and you will begin to see the dots form lines, circles, maybe even letters and words. Our desire to make sense of the universe leaves us with a legacy of false positives: hallucinations become ghosts and aliens; knocking noises in an empty house become spirits and poltergeists; shadows and light in a tree, or burn marks on a tortilla, become the Virgin Mary.
Science is simply our attempt to gain a greater understanding of the universe, and our place in it, by weeding out the false positives. This is done by finding some test for an idea, one that will either prove or disprove the idea's validity. For instance, we can look at a nightly log of police arrest reports over a period of months to see if there is a correlation between the full moon and antisocial behaviour.
It would be wonderful if psychics could actually help police solve crimes, if a forked tree branch could help us find water, if we could change the weather by doing a dance, or if we could understand our fellow man simply by knowing the exact time of his birth. No psychic has ever contributed to the solution of a crime, however, while DNA evidence has freed many an innocent person and convicted quite a few guilty ones; test wells and other geologic clues are more dependable ways to find water; thermometers, barometers, satellites and computers, while they don't allow us to control the weather, have led to a much better understanding of it; and talking to (especially listening to) one turns out to be a much better way of learning about and understanding each other.
There are many good books that talk about the importance of imagination, curiosity, and critical thinking to modern society. I have not read most of them, but of the one's I've read, I highly recommend:
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