When we do so, He can guide us as to whom we should talk to, when, what to say, what approach to take, and so on. While God can use us even when we are disobedient, He much more readily uses us when we are following His plan, in His power. If our words are truly His words, they will achieve His purpose, and their impact will be greater for being precisely the words that God knew our listener needed to hear. If our approach is God's, it will be more effective for going directly though whichever door is most open in the person's life. If our timing is God's, everything else will have more impact, since we will speak to the person when they are most receptive.
Prayer is the key to effective evangelism.
In prayer we find God's power, and no one will come to Christ unless God acts in His power. However, this does not mean that we should just ignore everything else. There are other things that are also important for effective evangelism. We must maintain a deep love for God. If we don't love God, we really don't have anything to tell anyone else.