The question assumes that evangelism is something that should be done, and rightly so. Jesus gave the command to his disciples before He returned back to his Father. Let’s first have a look at how Jesus worded his command to go out and evangelize: “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.” (Matthew 28:18-20).
These few verses teach us so much about evangelism. First, let your witness always be framed by the certainty that Christ has all the authority and that He is always with you, till the end of the age! Second, evangelism should be purposeful: it should be aimed at producing followers of Christ. Third, evangelism should have great content: we are to teach the commands of Christ himself. Fourth, evangelism is very broad, the Gospel is for all the nations on this earth. And finally, people who decide to put their trust in Jesus should be baptized in the wonderful name of the Triune God, as a testimony of all that God has done and will be doing in the life of the believer.
Take the audience into account
When you communicate the Gospel, it is wise to take the audience into account. Aim to evangelize intelligently. A great example of this is Paul on the Areopagus in Acts 17:15-34. The people of Athens love discussion and the exchange of new ideas. Paul tries to build a bridge to his audience by referring to the altar of the unknown god which he found in their city. His speech, or sermon, is quite philosophical, which suits his audience well. You should also be aware of how much your audience already knows. A Buddhist has no concept of a Creator God, so it is wise to start there. With a Jewish or Muslim audience, there will be much more common ground from which you can start to build.
Try to find a way of evangelism that connects with the needs of your audience. In the secularized and individualized West, evangelism through the Alpha Course seems to work quite well. Every evening starts out with a meal together and the evangelistic bible studies take place in a friendly, informal atmosphere. This might be just what lonely people are longing for. In a society with closely-knit communities, try to find a person who might introduce you to the whole community, or to a whole family.
Look for a way of evangelism that suits your own personality. Not every person feels comfortable with proclaiming the Gospel publicly and boldly. Some people are more like Andrew, the brother of Peter, who quietly introduced his brother to Jesus (John 1:40-42).
Evangelism can be very hard. Sometimes people seem to be so unresponsive, even hostile. Remember the parable of Jesus about the four different kinds of soil (Luke 8: 4-15). There is soil with lots of rocks in it, and there is good, fertile soil. Just be like the sower who sowed the Gospel everywhere; God will give fruit as it pleases Him. Try out different ways of sowing, don’t be discouraged if one particular approach doesn’t work.
Let your witness be soaked in prayer (Ephesians 6:18, 19). Ask God for guidance whom to talk to and in what way. Allow the Holy Spirit to lead you. Be prepared to jump at opportunities, even when they pop up at inconvenient moments (Ephesians 6:15). And, make sure that your words are backed up by a lifestyle which puts Christ first!