To evangelize about faith you need to understand people's spiritual interest and back grounds. Not everyone will respond to the same approach. Some need a strong debate, some need a gentle conversation, some need to see you live out your faith, and some need something completely different. The reality is that no one can change how another person believes. Only God can do that, but you do have a role to play by living out your faith and telling people the truth.
Learning a person's background requires building trust and a real relationship. There is no technique that can be taught to make that happen. You either connect with people or you do not. If you do not, then do your best to live out your faith in front of them, tell them the truth about Jesus, pray, and trust that God will send someone else to connect with them.
Evangelism needs sensitivity. You need to be sensitive to hear the Holy Spirit's direction. You need to be sensitive to the person's experiences, but that does not mean that you are not upfront and honest. It is all about the body language and how you present the truth. Your evangelism style needs to reflect God's love in a way that the recipient can hear it. It does not mean that they will automatically accept it.
Ask questions to get to know people. Ask them about their church background, where they attend now, and if they are a member anywhere. Church hurts can cut the deepest and last the longest, so you need to be careful with how you proceed when dealing with that. Prayer may be the only answer. However these questions will really help you know a person.
The last thing you ever want is to come across threatening as a Christian. No one is interested in what you have to say if you scare, threaten, or are rude to them. Before you go out make sure you pray especially if you are in a bad mood or had a hard day. You may come across differently than you want to be perceived.
Remember if Godsends you that means that Satan is tailing you. He will do his best to get you to get in your own way. Do not take people rejecting Jesus as personal rejection. It is hard because Jesus is so much a part of your life. Jesus is strong enough to take it, so give all your hurt feelings over to him.
Keep the first conversation simple and lay out your faith and why you believe. Save the controversial discussion for when you are prepared, ready, and already have a relationship. You want to always leave the door open to talk more about Jesus. Go in too hard too soon and the door can be slammed in you face.
Proverbs 3:5-6, Matthew 17:14-20, John 3:16-17, Acts 1:6-8, Romans 10:5-18, Ephesians 2:8-10, & Hebrews 11:1-3