The easiest way to invalidate a theory is to see what predictions it makes, and to figure out where those predictions were wrong.
One recent example: the choice between austerity and stimulus, in the US and Europe, shortly after the 2008 downturn. Keynesian economic theory claimed that if your interest rate approached 0%, that you could no longer stimulate the economy via interest rates, but that the best way to improve the situation was for the government to create and spend money. And that doing so wouldn't cause sudden inflation.
Another theory said that fiscal austerity measures and the reduction of government debt would improve the situation. This theory also suggested that the US should experience strong inflation in the years immediately following 2008.
IIRC, the US government spent something like 1/3 to 1/2 the money that some Keynesian economists recommend spending on a stimulus. Other countries tried varying degrees of austerity. So to test the theory, you'd need to compare what happened in different countries.
Note that this particular "Keynesian" theory does not necessarily recommend heavy government spending when the Fed interest rate is above 0%. Basically, it's only about emergency measures when ordinary economic theories have failed.
For an easily-accessible version of this particular "Keynesian" theory, and why it's supposed to work, see this paper on the "Capital Hill Baby Sitting Co-op": http://www.eecs.harvard.edu/cs286r/courses/fall09/papers/coo... This is really more of parable than anything else, but it explains the logic.
Tl;dr: At the government's scale, money is a weird abstraction and you can't always pretend that it works like grain or cars or other simple economic goods. Or to put it another way, if the economy gets bad enough, then everybody wants to work more hours at the restaurant, but nobody wants to go out to eat—and therefore something has to give.
I'm not qualified to comment on whether this theory is actually true. But that's how you might test it, and an explanation of why it's supposed to be useful under certain circumstances.