Consider a question in the light of a conclusion, theory, or argument that seems right.
The theory ought to be supported by examples, certainly, and perhaps other premises as well. Think of those.
Examples may be actual – bits of evidence for the theory. Or they may be hypothetical – possible instances that would support the theory if true.
Having brought to bear your own resources on the question, seek out other sources that yield examples and premises and defences of the theory, where those responsible for them have experience pertaining to, or have invested time and thought in, the question at hand.
Particularly seek out sources provided by those whose quality and quantity of experience or thought equals or exceeds your own, or whose different perspective casts the theory in new light.
Consider the credibility of those sources, on balance, in terms of their merits and demerits: what factors count for their veracity, and what factors count against.
Now dash the preferred theory against the rocks of doubt:
The best starting point is the counter-example, one that doesn’t support the preferred theory. Look hard for those. One valid counter-example forces a revision or qualification of the theory.
Consider alternate answers to the original question, and then look. (another way of getting at counter-examples).
Take a modal approach to truth – if there is no actual counter-example, is a counter-example possible? Even if it is possible, it ought to moderate the original, preferred theory.
Bear in mind that negation makes no difference to an argument in terms of its evidence, examples, and counter examples. That is to say, an argument of the form ‘not-p’ ought to be examined and tested in exactly the same way as an argument of the form ‘p’. (This is the case because the form of the argument is usually a semantic consideration – an argument that looks like ‘p’ can usually be reformulated as ‘not-p’, and vice versa).
Consider assumptions that underpin the preferred theory and its premises, and the alternatives to these (if an assumption is ‘p’, consider ‘not-p’, if ‘not-p’, consider ‘p’).
Consider how world-view might prejudice the fair examination of the theory and contradicting alternatives, and test the preferred theory against other world-views, holding your own in high suspicion. Would this theory necessarily still stand if I lived two thousand years ago or two thousand years hence? What is being sought here is a crack in the theory, not necessarily a definitive over-turning – just enough room for doubt that should prompt the introduction of caveats on the original claim.
Consider values underpinning the preference for one theory or argument holding true – why is the preferred case the preferred case? This is a way of interrogating ones own credibility. While doing this, may as well look at what you stand to gain from the preferred theory turning out to be or being held to be true (even if it’s just peace of mind).
Consider the rigour of the method of inquiry applied, and limitations on it, and either remedy problems or recognise constraints.
amending the theory:
Look at the original theory and give it due qualifications and caveats in light of doubts that have been turned up, balancing its merits against countervailing elements. Does the theory still stand outright? Is it demolished, or compromised, by actual or possible counter-example, and the possibility or likelihood of the truth of an alternate theory? Moderate the claim accordingly.
In writing up, don’t hide the process of developing and interrogating the theory by which a final conclusion has been formulated. To speak to this process directly can make the argument more lucid, more credible and more interesting: report the steps taken, twists and turns in terms of surety and confidence, and lack thereof, establishing of supporting points and doubts.