A.(not foolproof way) The way that I have been taught is via "the literature" in short, but essentially, if the theory is backed up by the conclusion of a paper, and the theory (or a paper concluding that the theory is correct) is widely cited, then the theory is judged to be reliable. These theories will still have hedged language in papers (could, should,probably and so forth) but in science outreach and general discourse there will not ( proven science, established, reliable, correct etc.). If one asks another for evidence, the expectation is a reply with a pointer to "the literature" rather than a particular repeatable experiment or observation that they have done. This is also judged to be an objective way (It is only as objective as the group of authors and peer reviewers of the papers are) and it is judged to be soundly based on only repeatable experiment or on new facts that the theories may predict correctly (most peer reviewed papers have little to no direct reference to either factor)
B.(foolproof way) I have used this way since I have discovered its power back in 2012. First of all forget any pre-conceived pet theories. Then when looking at an established theory, avoid until a much later stage the idea of needing to *replace* an established theory. This way is to find where the established theory is probably wrong, and why it is wrong, not to suggest that the established theory should be overturned. We are looking at negative results - experiments that are repeatable that do not match the established theory and failed predictions thereof. Then we look at the *chain* of evidence for the established theory. To speed this process, we have to work back on the trail of citations to an early part of the theory and then to whatever process of formulation was used initially to produce the theory, and then to the fewest assumptions used (parsimony). Check that the assumptions were not and still are not, amenable to direct experimentation or observation. Check whether the negative results were available when the theory was formulated. Then cycle through the assumptions starting from the most arbitrary to the least and check the *sensitivity* of the negative result to each assumption. Do this for any negative result that you can think of. Choose the assumption that the negative results are most sensitive to. Consider this assumption wrong and start a search for a suitable spectrum of possible replacements *for the assumption*.
Invariably there are *No* papers to help you in this process B so don't look for them even though the arguments of A demand them. In terms of looking for the "spectrum of alternatives to the assumption", anything that refers to any options online to the assumption or the conclusion of an alternative theory is worth looking at. When looking at an alternate assumption, try to use all the arguments, methodology and mathematics of the established theory apart from that linked to the assumption. When looking at alternative theories, first make sure the argument is *coherent* such that there is flow from the assumptions to the conclusions of the alternative. If there is not, disregard the incoherent aspects of the alternative theory concerned. If there are coherent aspects of an alternative theory, track back to the simplest assumptions and compare notes to the established theory. Take note of the *alternate assumption*, not any other aspects of the alternate theory. As an example, I have successfully extracted some useful alternative assumption from "creation science" without needing to take other assumption unrelated to the wrong assumption of an established scientific theory.
There you have it. Challenge me with an example of an established scientific theory.