How do we influence such a large world? One person at a time. One moment at a time. God has given us the privilege to carry His message to the people around us. We all have spheres of influence that we come in contact every with day. (School, work, family, friends, etc.) And this is where we can have the greatest influence.
Influence can happen quickly or may take years of relationship to happen. I heard a story about a man named Andrew Murray, who prayed for a close friend for 20+ years before he came to know Christ. We don't know God's time table, we just need to be faithful with the spheres He has put us in.
Also, let's not sell ourselves short to the amount of influence we have. Believe it or not you have the Creator of the universe who's got your back. He's the one who works through you anyway. Is it possible your idea of influence is too small? I can't answer that for you. But remember to be faithful with the small things in life. That's how you get to the big things.