For many, this is a question that provokes fear. Sharing the gospel has been understood as needing to have a high level of Bible knowledge to be prepared to answer any questions that might arise in the course of a "study." Evangelism has been seen as sharing the "facts of the Bible" with a person. This leads to fear for some, because they do not believe they have enough Bible knowledge or the ability to locate particular verses or passages when needed.
But this is not how the Bible presents evangelism and sharing the gospel. Yes, there are instances where the gospel was preached and conversion resulted (though these passages only fit our modern idea of "mental assent" to the facts of the gospel when forced into that paradigm). However, when we look at the way that the apostle Paul, for one example, describes how he shared the gospel in his ministry, we see a different idea emerge for how the gospel can be shared.
In short, we share the gospel by sharing our lives with others.
In 1 Thessalonians 2:7-12, Paul reveals that his ministry among the Thessalonian believers was humble, caring and encouraging. He came across to them as a gentle mother and a caring father. They were very dear to him. His work among them was characterized by these traits. His teaching was understood in these terms. He did not "convince" them of a series of facts; rather, he taught them the sacrificial way of Jesus by his own sacrificial way of life among them.
In 2 Corinthians 6:11-13, Paul speaks about his ministry among those believers in terms of deep affection. His heart was wide open to them; he had no restriction in his affection towards them. He considers them his children. In this way, he shared the gospel with them by sharing his own life with them.
How might you understand sharing the gospel with others differently if you see it in terms of sharing your life with others? How can you teach others through your example? How can the love of God flow through you to others in ways that reveals that love to them? How can the sacrifice of Jesus be made real in your life for the sake of others?