I cut my teeth on this approach because I went to LSE in the 1960s and met the key critical rationalist -- Popper (see some links like this one on falisification, or this more general and pretty bland one on the Great Man, or this brief essay on the basics). Even more impressive was his sidekick Gellner (a social philosopher of very broad scope -- see the Gellner homepage -- but my favourite work is the hilarious demolition of linguistic philosophy Words and Things -- I have a brief extract here). These two had a reputation for being really spiky critics. We can borrow some of the techniques for our much more modest task.
Critical rationalists like plain speaking, simple argument and above all a clear commitment to being capable of being wrong. Wearing your critical rationalist hat, you will insist that complex argument is translated into much more simple terms (or do this yourself of course). If you do not understand some sentences it is NOT because you are dense but because THEY have not formulated their views clearly! Above all you will want to ask yourself the key question about any statements -- are they scientific or non-scientific? If they are scientific they will actually be involved in making some concrete prediction about social events, now or in the future. This prediction will be risky -- in other words, evidence might come in that show it is wrong (that it is falsifiable in the jargon). There is no shame in being proved wrong. A calm objective scientific outlook will be equally interested in the wrong result as in a right one -- because you can learn from wrong results, think about where you went wrong, and try again.
However, far too many spokespersons, experts, researchers and policy makers do not want to risk being proved wrong and will do much to avoid it. So they cover up. They choose deliberately vague or obscure ways of saying what they believe, quite often by shrouding everything in appalling jargon, pious hopes or various pathetic appeals for us to trust them They have all sorts of secondary explanations up their sleeves just in case things do go wrong, and they can explain away any failures or problems. For example, things have changed in ways beyond their control, they haven't received enough support, we haven't given it enough time, all it takes is belief in ourselves, God moves in a mysterious way, it is we critics who are to blame and why are we being so negative.
A critical analyst must not let them get away with this. They take their sceptical eye to any general statements and ask what exactly is being stated or predicted here, behind all the rhetoric. They demand evidence. They try to think of a way in which statements could be put to the test, and ideally proved to be wrong.
EXAMPLE: A sports development policy-maker is trying to drum up support for public investment in hosting a mega-event. There is a lot of flag-waving and appeals to our patriotism, and also a lot of apalling management-speak about 'investment matrices', 'contingency management', 'drivers', 'double-loop learning' [is that still fashionable?] and 'rolling out micro-managed studies at the stakeholder interface'. Our critical rationalist patiently reads all this stuff looking for some concrete statements about benefits to be gained and might even helpfully suggest some nice specific tests:
Any veterans of methods courses could then proceed to ask suitably specific questions about samples (random? stratified random? sample biases? response rates?, controlling variables and test design to eliminate 'confounding' or 'spurious corelation', tests of significance if any, whether the data can be used to test theories, whether any raw data is included so we can check the interpretive processes) and so on.
how exactly are 'members of the community' to benefit -- will their life expectancy increase?
who exactly are 'members of the community' for that matter?
what would count as 'success' in sporting terms -- more medals per entrant?
how could we be sure 'national prestige' had increased -- more visitors to Britain?
In general, critical rationalists believe that the role of the critical public is crucial, which is why material must be made publicly available -- not just finished results but as much information as possible about the empirical work including the design of the research and its actual conduct (including things like how researchers and/or coders were trained) . The very useful BMJ checklist for health evaluation studies here might be generally applied, although we have to remember that the preferred design in much health research is a very strict one -- the random controlled trial
Any approach that suggests we must just trust the researcher is suspect. It is not that we do not trust researchers, but that no-one can fully control their own impliciit biases and preferences. Although critical rationalism would not always choose a 'scientific', quantitative design, it would expect a lot of disclosure from other approaches like ethnography