With over five years of experience preaching the gospel of God's grace to strangers in streets, university campuses, and marketplaces, I can safely admit that I've had to learn the hard way, having made many mistakes. My purpose is not to write a list of practical "How Not To's", but "How To's" with a few "Not To's" included.
So here it goes:
1) Study your Bible with a heart to love, revere, worship and obey God before trying to teach others. Remember your priorities: God made all of us, and it is therefore God first, God in the middle, and God last. God in Christ is our primary object of love, knowledge, obedience, respect, and authority. He is our Sovereign LORD to whom we owe complete loyalty. When we see God as He has revealed Himself in the gospel of Christ, and He really amazes us, we become all the more persuasive toward outsiders. (The Holy Spirit is He who converts people, however, we are responsible under God's Sovereignty to strive at being persuasive by His grace within us).
2) People can sense your attitude, despite how "right" you are. If you want to persuade others of the beauty, sweetness and love of God's grace through Christ, then show it both with an attitude and by words that are genuine and full of grace (see Colossians 4:6, “Let your speech always be gracious, seasoned with salt, so that you may know how you ought to answer each person”).
The message of the cross is offensive to natural sinful people, but the messenger does not have to provide backing to their revulsion by exhibiting unattractive behavior and manners himself. In support of this point, carefully read Romans 12:9-21; Ephesians chapters 4-6; Colossians chapters 3-4; Philippians 2:1-15; 1 Peter 3:8-22; 2 Peter 1:5-8; the book of Proverbs, especially noting those that speak of the use of the tongue; etc.
3) Just to emphasize and build on that last point, think about how you yourself speak on a daily basis, and then think about what the Bible says about how we should use our speech. Take Proverbs 12:18 for example: “There is one whose rash words are like sword thrusts, but the tongue of the wise brings healing.”
In other words, if you are wise you will speak words that will help, comfort, heal, and give life, not words that will harm or hinder the spiritual health of your hearers. Doctors don’t needlessly criticize their patients and then intimidate them into accepting treatments. That would be ridiculous! (This is clearly one of the “How Not To’s” I said would be mentioned, and it’s worth repeating! So, speak courteously, as befits a winner of souls. Too many of us are already experienced enough at failing with this.)
4) Don’t put the gospel through a cookie-cutter. The gospel is a glorious, magnificent, world-tilting message of truth, salvation, love, promise, and glory to the repentant and humble, and God has given 66 books in our language to teach it to us. It can be explained from many different passages of Scripture, so I recommend getting real familiar with some and using them often. You can read Matthew 5-7 and Romans 1-8 for a number of useful texts. But also use a variety of other passages whenever possible, or when a different situation calls for it. You may not have time to give a full presentation of the gospel in every situation, so be ready to be clear and helpful with whatever you can say.
5) Each person you meet is different, so I believe you can preach the good news in a different way to everyone you meet, depending on individual needs. To illustrate this, let’s say you meet Sally from the local baptist congregation. She grew up in the church and never thought of herself as anything but saved, yet she doesn’t seem to have come to grips with how great her sin and her need for a spotless sacrifice really is. You will preach truth to her according to what she needs to know about the gospel, which she may not have grasped yet. Next you meet Mohammad, an immigrant Muslim. Now things are different. Mohammad, on the other hand, doesn’t think of God, sin, or salvation in the same way you do. You may have to define what you mean by your terms, such as repentance, justification, mercy, justice, the Triune nature of God, the deity of Jesus, and so on, before Mohammad can grasp what must be accepted for true light and life. Don’t change the message of the gospel, it is the same for both, but change the method. Speak to Sally and Mohammad according to what they need to come to terms with.
This list was inspired by another list that I read from theCripplegate.com, called Street Evangelism in Six Steps.
Also check out An Alternative to Cold Evangelism.