Here is my response to the questioner:
I am wary of your question, because I mistrust proselytizing of any kind, theistic or atheistic. Having said that, here are some things I know about the art of persuasion. An agnostic myself, I have Christian friends, so I know a little about how they tick.
First of all, I wouldn’t use the words from your question. Those words would turn a theist right off to anything you have to say. The word make implies coercion. Escape implies that they are trapped. A theist doesn’t feel trapped. They report a sense of freedom. Actually, they see others as trapped in their own non-theistic world views. They don’t consider themselves deluded and the word is derogatory. Inviting a theist to consider the possibility that there is no God is more enticing and respectful.
My next point is a crucial one: you cannot change someone who doesn’t want to change. Do they want to change? If not, you are wasting your time.
Ask yourself why do I want to change someone’s beliefs? Is it necessary? Why is it necessary? How does it help the other person? What do they stand to lose? Am I being kind? Am I being respectful? What do I get out of it? An honest evaluation of these questions will make you more effective. If you see real benefit in the person changing, then use it as a carrot to entice them.
Rapport is an important component of persuasion. It makes the other person feel understood and respected. They will be more open to what you have to say. Whenever possible, use their language. Learn what you can about their beliefs and show them your knowledge of those beliefs. It builds a bridge.
Set a good example. Actions speak louder than words. The example you set is more influential than what you say. If you are a dick, it doesn’t reflect well on atheists. If you are kind and generous, the theist will see that atheists are good people too. You catch more flies with honey than you do vinegar.
Be a friend. Change takes time. You will have more influence as a friend. Be patient. Rushing someone makes them dig in their heels.
It is possible that some theists could never be persuaded. One finding of moral psychology is that people are born as conservative, liberal or libertarian and rarely change affiliations during life. Could people also be born theist or atheist? Brain structures responsible for religious experience have been discovered. I speculate that genes are involved in the expression of these brain pathways. In other words, I think that people are born as theists or as atheists. If so, your job will be that much more tough.
Here are some articles about the brain networks responsible for religious experience:
©2016 Stephen L. Martin
Painting: Excavation by Willem de Kooning