Randomized controlled trial
A randomized controlled trial (RCT) is a type of study that tries to evaluate a particular treatment or intervention, usually in a medical field. It is considered the most powerful and convincing form of evidence in medicine because of the number of variables that can be controlled.
A basic RCT requires that a group of people be split randomly into two groups. One group receives the treatment under scrutiny, the other receives a suitable control. The performance of the two groups is then compared to see if the new idea is worth adopting on a wider scale. This isn't a new idea, a similar method was described in the Bible and is dated to around 600 BCE. However, it is only relatively recently that the idea has been applied to medicine.
One of the main ways that bias can creep into a medical trial is by insufficient randomization. This is because doctors can, subconsciously or intentionally, influence which patient can go into which group. Researchers who are aware of the medical history of their patients may put the ones most likely to respond in the group to receive treatment, and those with a low probability of response in the control group. This will unfairly skew the results and make them less applicable to a wider scale. Even coin tossing or "apparently" random selection methods such as date of birth still allow bias to creep in. Therefore, the only sufficient way of randomizing a sample is independently and by a computer algorithm.
To just administer a group of people a treatment gives no useful data, such as with the Fish Oil "trials" to test if they improved the performance of school children. An RCT therefore splits its participants into two groups, "A" and "B." One is given a treatment and the other acts as a "control," that is, a group that where the outcome is known. Importantly, the control group isn't just given "nothing," as anything will usually do better than nothing. The control group is usually given a placebo, to determine if the clinical effects are real or due to the placebo effect. However, as many active drugs are likely to be better than placebos (as well as the ethics behind using placebos), the control group can also be given a medication that has a known effect. This option also provides the advantage of allowing a comparison between a current treatment and a new treatment, to see if a new treatment is worth adopting.
One of the more important aspects is blinding. This is where a patient is unaware if they are receiving a real treatment or a control treatment, thus preventing the placebo effect and the patient's expectations from skewing the result. A group of patients who are told they are receiving a new treatment are likely to respond more positively to it, therefore it should be hidden from them. Similarly, the researchers themselves should be blinded. This prevents researchers from redoing or reinterpreting data to suit their interests, even when it isn't intentional or malicious. To be utterly complete, the blinding should not allow anyone to know that two people are in the same group (even if they don't know what that group is). If the memberships of the two groups is known, the probability of having a positive result can be as high as 50%. Some studies even indicate that a doctor can subconsciously transmit the idea that they are administering a placebo if they are aware of it. When both patient and researcher are blinded, it is known as "double blind" and this is virtually the only form an RCT will take.
Proponents of alternative medicines often claim that RCTs are not good means of testing their wares. Ostensibly this is because RCTs invariably show that alternative medicine isn't effective — indeed, if an alternative medicine is shown to be effective by RCT, it ceases to be "alternative" and merely becomes "medicine." There are numerous specific claims, from the claim that "there's more to life than evidence" to the idea that certain alternative medicines like homeopathy can't have proper placebos generated for them. Given that even very theatrical placebo operations have been carried out to test the efficacy of key-hole surgery, there are clearly very few things where a suitable placebo cannot be devised.
 Use outside medical research
Noted woo-exposer Dr. Ben Goldacre has argued that politicians ought to use randomised controlled trials for testing their policies. For example, a proposal to decrease class sizes in schools to increase educational performance, could be tested by dividing a group of schools into two subgroups at random. Dr. Goldacre has expressed frustration that politicians seem to think implementing a policy without any scientifically-gathered evidence behind it — or even in defiance of all the evidence — is perfectly fine.
Ironically, RCTs already have been used in developing countries in this way, but are generally politically "unthinkable" in developed countries. (Literally, in some cases, because some politicians and policy wonks don't know what randomised controlled trials are, or at least don't realise that it would make sense to use them for testing public policies.) Small trials used by governments to "trial" their policies are generally not randomised controlled trials. Arguably they have nothing to do with science, and everything to do with optics and making heuristic adjustments to the implementation of a policy, rather than the policy itself.
Doing politics via experiments raises serious ethical issues. However, simply subjecting an entire population to a new policy on the basis that "my buddies in the think tank paid by multinational corporations assure me it's a very good idea, and we can sell it to the electorate in such a way that it polls tolerably well" arguably also raises serious ethical issues. Especially when those same corporations stand to benefit handsomely from the policy (regulatory capture) — but hey, how likely is that, right?