First and foremost, it isn’t your job to “win souls for Christ”. That is the job of the Holy Spirit. Read Matthew 13:18-23, the Parable of the Sower. Nowhere in that passage, or the corresponding ones in Mark and Luke does Jesus state that it is the sower’s job to make the seeds grow. His job is just to sow the seeds. So too is it with evangelization. Your job is to just tell the truth in love and humility. However, that doesn’t mean that you can’t use some “techniques” to get people to think about their position on Christ. The one I like is the one Christ often used Himself when faced with opposition to who He was.
Whe the Pharisees tried to discredit Him in public, they asked Him where He got His authority to preach from. Jesus simply turned the tables on them and asked where John the Baptist got his authority from. Since He knew they really didn’t know, they left Him alone. You can use a similar tactic. The principle is that whoever is asking the questions is in control of the conversation.
Here is a simple conversation that demonstrates what I am talking about.
John: Why do you believe in all this Jesus nonsense?
Me: Why don’t you believe in it?
John: Because there is no God, that’s why. Jesus must just be a myth.
Me: Why do you say there is no God? Can you prove it?
John: Well, no, I can’t actually PROVE there is no God. It’s just what I believe.
Me: An what information do you base this belief on? Is it facts, or the opinions of people who you think are really smart?
That is a short, lame example, but you can see the highlights of what I am saying. Put yourself in the position to ask the questions and make the other person justify their non-belief. Do it with kindness and compassion, but you also need to be prepared to answer their questions when they come up. As it was posted before, pray. Pray hard, pray often. Ask God to make you a vessel for His work. Then study. Get a copy of the Revised Standard Version - Catholic Edition and the Cathecism. Start there and then go to Catholic Answers and buy the Beginning Apologetics series.