By learning to think critically, which is a talent you do not possess. You hear PETA telling you themselves how wonderful they are. You hear other people showing evidence of their misdeeds, in some cases public records whose validity is not rationally in dispute. What is the proper critical approach here? Do you think the bad things about an organization, which are true, will be published by the organization? Does the mere fact that someone opposes an organization make them biased such that their reasons for opposition become invalid?
You have PETA's very large public relations department telling you how, sadly, some animals are simply beyond hope and must be euthanized with great sorrow and sadness. But in contrast you have ex-employees swearing affidavits stating under penalty of perjury that PETA made them kill perfectly good animals. Which is most likely to be true? How would you know that?
