One To One
As the Lord's Ambassadors, we are called to be His witnesses. What a glorious honor to proclaim the mystery of the Gospel. One on One witnessing is a very effective way to fulfill the great commission. Think about it the Lord has placed you in unique situations and circumstances unlike any one else. You will have opportunities to share with people that no one else would.
What are some basic ideas to help you? One is to use tracts as a means of an ice breaker. So many times if we could just get the conversation started we would be able to share with them. How do we overcome this? Tracts are a unique way to do this. Simply hand the person a tract, tell them it talks about eternity, have them read it and then ask what they think about it. In this situation, use tracts that are fairly short, but clear and Biblical. After they have read it see what they think and be prepared to give an answer for the hope that is in you.
Another way that I have found to be effective is to ask them a general question in regards to spiritual matters. In other words bait the hook and throw out the line to see if they are biting. For instance, asking them if they ever think about eternity and where they might spend it, is a very general non-offensive question that will help you discern if you should go any further, etc..
If someone is open, perhaps start out by sharing your testimony and then use Biblical principles to show them their need of Christ. The principles I'm speaking of are; man's original righteousness-Gen 1:26-27, man's fall from righteousness-Gen. 3:9-10, man's attempt at righteousness through religion--Romans 10:3, the law which reveals our unrighteousness-Rom. 3:19-20, Gal. 3:24, and then God's gift of righteousness--Romans 5:17-18.
Please see the article on "Righteousness is the issue" for help in understanding the principles of witnessing. May the Lord bless you in your efforts.