1) Make emotionally persuasive arguments (just as theists do) to dissuade people from believing or to question their beliefs. E.G., slavery, mysogeny, original sin, empty sacrifice, child molesting clergy, money grubbing churches, etc.
2) Make well reasoned arguments against gods unlikely existence. E.G., scientific explanations, bibilical errancy, biblical revisionism, uselesness of intercessory prayer, the triune god, exclusivity,
Not everyone is on the same intellectual level so the approach most effective will vary.
Some will misunderstand this as an attempt to convert people to atheism. The overall goal is not to convert people to atheism, but to get people to think critically. To introduce people to the silly and absurd problems with their beliefs whether they be a theist or an atheist such that they learn to use the tools that will protect them from credulity or error in the future.