By scientific testing. If you have a control group which does not meditate and another group that does meditate, and the changes occur only in the group that meditates, then it is evidence that the meditative state is the cause. Further testing with greater control of the variable (whether the people are meditating or not) will give more accurate answers.
For the sake of simplicity, I won't get into the issues with NHST and other problems (mostly placebo related) as to why this doesn't work as well as we'd like. But before I get into the real issues:
Really, science isn't that hard.
Now you're just insulting me!
Let's examine scientific testing. I'm not going to check my memory here, but I believe it was oddly enough exactly a century before Einstein's 1905, Nobel Prize winning work on the photoelectric effect that Young "proved" light was a wave. He demonstrated that light behaved in ways that no particle could (although Newton's reputation and preference for the particle/corpuscular theory of light made acceptance of Young's view take time). By the close of the 19th century, not only had Young's view been vindicated but the notion of light (and the electromagnetic spectrum) as consisting of waves was central to physics. A century of scientific testing had shown that not only was light a wave, but it was so definitely a wave the most successful framework in physics since Newton's mechanics required this (that framework being electromagnetism).
Then, in 1905, Einstein showed that light was composed of particles.
If scientific testing were as simple as you state, physicists would have laughed at any attempt to restore the "corpuscular" (particle) view of light. Einstein would have been dismissed. But let's imagine that some scientists, wishing to show him to be wrong rather than rely on established "fact", decided to put his explanation of the photoelectric effect to the test (which was done, actually). They would find evidence that Einstein was, indeed, correct: light is made up of parts. But this presents a very, very big problem. After all, a century of scientific testing and indeed a central theory to all of physics (at the time) held that light was a wave. Now, "The Scientific Method" (which we don't actually practice, at least not as taught) holds that this means we have to perform tests to see which of the opposing hypotheses- light as a wave vs. light as a particle- is the correct one. If scientists had actually done this, had actually followed the naïve, simplified "scientific method" taught in primary school and to undergraduates, they would still be arguing to this day over whether light was a wave or a particle. Luckily, the question was so simplistic and the evidence so clear that, despite the best efforts of the greatest physicists of the period, only one conclusion was possible: any scientific test to determine whether light was a wave or a particle was bound to fail because the entire theoretical framework which stated that something could either be a particle or a wave but not both was ITSELF wrong. Completely wrong. Nothing was either a wave or a particle.
Unfortunately, things in the sciences are rarely so simple and clear when it comes between deciding whether the evidence you get is because you tested the right question the right way, or because your theoretical assumptions falsely dictated either how you would ask a question or how you would test it (or both) or even because your methods (statistical, instrumental, etc.) were flawed. Thus rather basic, fundamental theories over the nature of cognition which are mutually exclusive and incompatible have been tested and supported for almost half a century now (and the older view of cognition has been around since the beginning of the cognitive sciences).
The primary methodology used for scientific testing across the sciences (from particle physics to medicine to the behavioral sciences that begat the method) is NHST (null hypothesis significance testing, a.k.a. significance testing, a.k.a. statistical decision theory). It is the combining of two radically opposed approaches to statistics and data analysis (the approach of Sir Ronald Fisher on the one hand and Pearson & Neyman on the other) that has been criticized as fundamentally flawed since before its inception. It is the standard methodology taught to researchers today, despite the fact that the many, many hundreds of criticisms of the paradigm as fatally flawed go almost completely unanswered (or, in some cases, those trying to answer it, such as an APA task force, have been met not only by apathy but by the adoption of standard practices by the APS and particle physicists more generally of adopting this welding of two opposed statistical testing paradigms in the social/behavioral sciences).
Currently in the "hardest" of sciences (physics) there exists a fundamental dispute. It isn't over experiments or theory. It is over how to do physics and what physics is or should be. On one side are the anthropic physicists who believe that our best theories and evidence make it clear that there is no possible way the classical, reductionist model can succeed and no "theory of everything" that could exist. They regard those (an increasing minority) who stick to the goal of such a theory and the reductionist approach as one of basically religious bias (or something like religious bias). Those with ACTUAL religious bias accuse the anthropic physicists as opting for the anthropic solution over god because they are biased against anything resembling evidence for a creator. And the (ever-dwindling) supporter of the classical approach join those inclined to see evidence for a created or at least "special" universe in physics/cosmology in their critique of the anthropically inclined as too willing to accept mathematical aesthetics as evidence and too willing to opt for solutions other than our universe as "special" in order to bias the evidence by fixing the models/equations.
And an even fewer minority accuse basically everybody else as being too willing to see reality in the mathematical models that were irreparably separated from physical reality by quantum mechanics a century ago, a divide which particle physics, cosmology, etc., have only weakened (this is my position).
In the "hardest" science, therefore, we find as mainstream theories such frameworks as string theory, quantum gravities, inflationary cosmology, supersymmetry, dark energy/matter, and many more theories or notions lacking any empirical support and often even the capacity FOR empirical support.
Historians have more evidence, in general, than exists for M-theory or even any of the theories of gravitation.