The last few years have seen an explosion of interest in extreme event attribution, the science of estimating the influence of human activities or other factors on the probability and other characteristics of an observed extreme weather or climate event. This is driven by public interest, but also has practical applications in decision-making after the event and for raising awareness of current and future climate change impacts. The World Weather Attribution (WWA) collaboration has over the last 5 years developed a methodology to answer these questions in a scientifically rigorous way in the immediate wake of the event when the information is most in demand. This methodology has been developed in the practice of investigating the role of climate change in two dozen extreme events world-wide. In this paper, we highlight the lessons learned through this experience. The methodology itself is documented in a more extensive companion paper. It covers all steps in the attribution process: the event choice and definition, collecting and assessing observations and estimating probability and trends from these, climate model evaluation, estimating modelled hazard trends and their significance, synthesis of the attribution of the hazard, assessment of trends in vulnerability and exposure, and communication. Here, we discuss how each of these steps entails choices that may affect the results, the common problems that can occur and how robust conclusions can (or cannot) be derived from the analysis. Some of these developments also apply to other attribution methodologies and indeed to other problems in climate science.