Paul and Barnabas arrived at Pisidian Antioch, weary and aching from their perilous march through the mountains. Still, they wasted no time in making their way to the synagogue early enough to find a good seat to listen to the reading of God's Word. They made their destination by the Sabbath.
They said to Paul, "Would you like to preach?" That was his cue! (I can read the man's mind: I thought you'd never ask!) Without hesitation, he delivered the goods. He started in Genesis and preached all the way through to the ministry of Christ completely from memory! He had no notes. He did it extemporaneously.
The response was overwhelming. Luke informs us that the next Sabbath the whole town showed up to hear the message he would deliver. The same was true then as it is today: people are hungry for the Word of God. When you have hungry hearts and great food served well, there's no problem getting people to come for the spiritual feast. Finding people who long to be fed the nourishing meat of God's truth is no great challenge.
Therefore, my advice is simple: When you have the unexpected opportunity to share the good news, share it. But be careful not to dump the whole truckload. If you're sitting on a plane and the opportunity presents itself, don't preach through the whole Old Testament before getting to the heart of the Gospel. Tell that hungry soul how to find a piece of bread. As you lift up Christ, tell him of your own spiritual journey. If done courteously and interestingly, he will hang on every word, just as they did with Paul. And the response was overwhelmingly positive.
As Jesus promised, "When I am lifted up from the earth, [I] will draw all men to myself" (John 12:32 NIV).