If you do let me say read on a bit because I hope to help change your perspective on what Evangelism is all about.
Those who had the memories of the type above will be happy to know that most of Christianity doesn't see evangelizing the world in quite the same manner. Now you might be thinking well I don't know of any other forms of evangelism and you sadly might be right. You haven't likely seen a true Evangelist do his or her thing because either one it was very subtle or as is the case for the other part no Christian has taken the chance to share the Gospel of Christ with you.
So what exactly is evangelism supposed to look like? Well first before answering that let me say that to those who are Christians we need to take more seriously the words of Jesus in the 28th chapter of the Gospel of Matthew when He says,
"Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you."
Matthew 28:19-20 NIV
These words weren't merely a friendly suggestion of the type of things we should be doing but its okay that were not doing it. These were more than suggestions or options for the Christian, these were plain and simply Commands from our Savior and we would be wise to heed the command of Him who knows best how to reach a people in desperate need of His saving grace.
So now that we know that its a command, what does this look like? Well quite simply put, Evangelism is about relationships. If I asked you the question, "Would you marry someone you just met that sat down next to you at Starbucks?" how would you respond? Most sane people would respond with a resounding "No". What if I asked, "Would you marry that same person you met at Starbucks and had a conversation with for 30 minutes?" how then would you respond? Probably in the same way. Marriage is a serious commitment. What if I asked you, "Would you respond to an invitation to accept Jesus as your Lord and Savior from a complete stranger, someone you have never had any dialogue with, and not to mention you don't even know who Jesus is besides a cuss word." How would you then respond?
Remember when Evangelizing its about building a relationship. The mission of Evangelism is certainly spreading the word and helping to "convert sinners into winners" eternally but can this be done by force or by a one-time conversation from a stranger? Not likely and if you think of your own experience with coming to a saving knowledge of Christ, you likely didn't do so after one experience. It may have been that one experience that started you off on a step by step path to discovering the truth of the Gospel but it was just one step in many that led to true conversion. If someone is closer to a decision for Christ then perhaps you can be the one to pray with them and witness their conversion but it would not have been without the hard work of others gone before you.
Also, be prepared to become a guide for the person seeking Christ. Be open about your faith but give room for the person to doubt, question and research the things that don't sit easy with them. Remember, a relationship with Christ is like a marriage and if that is the picture we get then certainly it is a good thing that much thought and study go into making a decision to follow Christ. This is why many people, not just Pastors get to witness conversions. Any who labor for the Gospel will have their part, whether emotionally, prayerfully or intellectually, in the conversion story, none is more important than the other. The important thing is to focus on the task of reaching and reasoning with the unbeliever and being relational with them. It is hopefully through this process (which takes years sometimes) that we can see souls won for Christ.
So in closing, when Evangelizing to the world (a clear command from scripture) keep in mind that you don't have to get a prayer, or a conversion every time you talk with someone. Its not our job to do the saving, that's God's work but we would be wise to take a tip from Paul in regards to Evangelism when he said,
"I planted the seed, Apollos watered it, but God made it grow."
1 Corinthians 3:6 NIV
Be about the job of planting and watering the seeds of the Gospel and if you are faithful to the work you will see God make these seeds grow.