If you wish to explain some of your Christian beliefs, you should also show a genuine interest in the beliefs of your atheist friend. Of course, your friend may or may not wish to share his or her beliefs, but an expression of genuine interest and a patient willingness to listen and to understand will go a long way. Trust will be engendered when your friend realises that you are not seeking to preach, but really do want to share each other's views.
The answer depends on what is the reason for a person being an atheist. As mentioned above, listening is a prerequisite, for any such conversation, as is caring about the person as a person for whom Christ died, not just as a number.
It would also be necessary to know at least in a general sense, the reason for a persons atheism. Most would know their own mind on the matter and it might be quite instructive. Many atheists have had previous church connections and have rightly been 'turned off' by very real wrongs done by persons claiming to be Christians. So understanding is important, as is the patience and the reality of personal faith, so that it can be demonstrated that you are not of that kind.
Objections to belief in God can only be dealt with if there is some degree of openness. This may not in reality be the case as, for many, but certainly not all, atheism is a choice to support a life in rebellion against God. Intellectual objections may indeed be real and can certainly be answered, but there may be every answer given and still a 'barrier,' as the atheism is essential to the life-style. In this case there must develop a sense of need, otherwise the Gospel is unnecessary from that persons viewpoint - even though the Christian can see its necessity. Certainly some knowledge of intellectual objections would help and this will also test if the person is fair-minded and searching or are unwilling to consider reasonable explanations.
Having a personal understanding of how faith in Christ relates to every area of life may also help, as would understanding flaws in major intellectual constructs which underpin atheism such as the theory of evolution, which is unsupported by science, but is essential to an atheistic world view.
Answer:
Consider how you would feel if the shoe were on the other foot. If one of your friends was a user of hard drugs, a swinger, Pastifarian (worshipping the Flying Spaghetti Monster), a member of the Church of the Subgenius (or any of the more mainline religions like Moslem, Hindu or Buddhist) and asked you to come to meet with him and his friends. Assuming it was pretty obvious that your friend fully expected that you would "see the light" and join up after this introduction. How would you feel?
The answer is obvious, a person prefers to find their own way in these matters. Leave your friend alone or you'll have neither a convert or a friend.
You might also ask yourself what an atheist would have to do to convince you that there is no God. An atheist will be as strong in his convictions as you are. What will you do if his arguments are better than yours?