If you don't know this person, ask lots of questions to get to know them. Then, ask a direction setting question about what they believe. Be creative, not awkward - ex. if I'm talking about baseball I will mention my favorite team, the Cardinals, and my favorite player, Albert Pujols. I will then mention how I respect him both for his baseball skills and because he is so outspoken about his faith. I will then ask what their perspective on spirituality and faith is. Once you are in a conversation about spirituality, ask them questions about what they believe (this is what the book Tactics, by Gregory Koukl, is all about). After asking the "what" questions ask "why" questions (why do you believe that, etc.) and finally leading questions (if you believe that, then...ask other questions that lead to the gospel). You'll find most people have no idea what they believe or why they believe it. Check out a revealing example of that in the video below:
The main point of this evangelism idea is get comfortable asking questions and learning to figure out where the other person is coming from. Of course you should make every effort to get through all 4 barriers but for this challenge, focus most on learning to listen and ask good questions. You'll be surprised how much fun you have. And don't forget, pray 1st and go in the power of the Holy Spirit!