It is very difficult for a constructive dialogue to take place if there is no common ground of understanding between the two parties. Before engaging in a conversation with a religious person, educate yourself on the basics of their beliefs. Especially if you are very unfamiliar with the person's religion, search online, read articles, consult books, and consider taking a look at the faith's sacred text(s). This will help you better understand where the other person is coming from, and will help you to generate questions about their faith. It is completely fair for you to expect the same of the other person. Offer to recommend some key atheist works that speak to your point of view, and ask the person to consult them to facilitate your discussion. You can always delay and resume the conversation at another time. Before you can explain to others what it means to be an atheist, you need to be able to explain it to yourself. You don't have to use a textbook definition of atheism there is no single "atheist" view, just as there is no single "Christian" or "Hindu" view. Come up with a definition that works for you. Before you begin the conversation, ask if the person understands what an atheist is. You may want to say, "I'm looking forward to talking with you about atheism. Before we start, why don't you tell me what you know about it." If they don't know anything about atheism, or assume that it means you believe in nothing or are satanic in some way, don't criticize them for it. Instead, quickly provide them with some basic information about atheism. You can start the conversation by saying, "Why don't I tell you a little bit more about atheism, so you know where I'm coming from." If necessary, provide some source recommendations for the other person to consult and request that you resume the conversation at another time. Make an effort to understand the other point of view by listening and asking questions. This will show that you are engaged in the discussion. If you don't have specific questions, ask open ended ones such as, "Tell me more about your beliefs" or "How did you come to believe what you do?" Listen when they respond. Make eye contact and focus on what the person is saying. Now is not the time to be planning your next question or trying to look up something on your phone. Don't ask questions that are purposely leading and antagonistic. For example, refrain from saying something like, "What makes you think your religion is so much better than others?" Instead, try asking, "What aspects of your religion set it apart from others?" This is a nicer way of asking the same question. You may think the other person's belief system is ridiculous, but offering ridicule will get you nowhere positive. Just because you may have read somewhere that there is a negative correlation between IQ and religiosity (that is, that less intelligent people tend to be more religious) doesn't mean you should make generalized assumptions or critical remarks about the other person being "foolish" or "delusional." Offer respect if you want to be given respect. Steer clear of open-ended or hostile questions that won't move the conversation along. For example, refrain from asking, "Why are Christians so crazy?" You're not only generalizing, but you're backing the person into a corner, as they couldn't possibly begin to answer your question. Don't blame the person for all the evils you believe have been done in the name of that religion. You don't want to be blamed for all the evils done by those who rejected religion, do you? You can ask, however, how their religion reconciles evil acts done under the guise of the faith. Don't just say you're open to learning something new; mean what you say. In learning more about other faiths, you'll only broaden your own worldview. If your beliefs will be threatened by knowledge, then maybe they ought to be reconsidered anyway. An atheist should be someone who is open to asking questions and seeking answers. Like a good scientist, an atheist should never be afraid of being proven wrong. Truth should be your ultimate goal. If the person invites you to a religious service, agree to go as a respectful observer. You don't have to convert to their religion or share their beliefs, but you will certainly learn something new. You in turn can invite them to a gathering of others like you.

Summary:
Do your homework. Define what atheism means to you. Ask questions and listen to answers with curiosity and respect. Avoid taking cheap shots. Be open to learning something new.