Of course, the bedrock of persuasion lies in being the kind of person that others will want to know and trust. When it is time to move beyond that foundation, what comes next?
Unlike some religions or denominations, we don't have a short and familiar canned speech, ready to go. Born-again Christians have John 3:16, which even many non-Christians can recite from memory, having heard it and read it so often whether they sought it out or not. Heathens have Havamal 76, which is as good a capsule of Ásatrú as anything I have ever found. Seeing it posted in bus stops would make my day.
So, Heathens: let's assume that you have engaged a willing person in conversation about Heathenry. They are likely to ask questions that are framed in a Christian context. If your conversation is adversarial, expect this to happen deliberately. But even a person who is truly interested may not know any other way to talk about religion. If they ask, "What does Ásatrú have to say about thus-and-such a question?" the best answer might be, "We don't think that question is important, or even meaningful, because we look at things in an entirely different way."
One stink we can easily steer clear of is anything that smells of "You must believe this way, or you are evil or lost or there is something wrong with you." You might even make a point of saying that we expect a world of many religions, and that's the way it is supposed to be. Heathenry is right for us; maybe it's right for you, too.
Perhaps you will be an instant success at this. More likely, not; at least, not right away, or even very soon. Keep at it, because you will get better. I firmly believe there are many Heathens out there, conscious or not, waiting to be found. And even those who are not Heathen can benefit from gaining a good understanding from us of who and what we are.