First thing: is it in The Goldilocks Spot? For this, do not look at the result itself, but look at the confidence interval around the result. Ask yourself two questions:
1. Is the lower bound of the interval large enough that if that were the true effect, we wouldn’t think the result is substantively trivial?
2. Is the upper bound of the interval small enough that if that were the point estimate, we wouldn’t think the result was implausible?
(Of course, from this we move to questions about whether the study was well-designed so that the estimated effects are actually estimates of what we mean to be estimating, etc.. But this seems like a first hurdle for considering whether what is presented as a positive result should be interpreted as possibly such.)
Caveat: Note that this also assumes the hypothesis is a hypothesis that the effect in question is not trivial, and hypotheses may vary in this respect.