How do you go about answering a question like that? Some people might take it lightly, and say:
There's another question always lurking behind the first: Why? Why is that your goal? It's your whole life. It's everything you've got. But no matter how you invest it, one day it will be over. You'll be gone. Then, eventually, after a few years or a few hundred, you'll be forgotten. Will it make any difference whether you had fun, whether you retired at 50? Finally the earth will turn into a cold, dead lump, or will be incinerated like a piece of tissue paper in a great flash of fire.
If you ever consider questions like those, you must have an opinion about whether God exists. If there is no God, it simply doesn't matter. You can please yourself. Or you can not please yourself. You can be one of the many people who pursue what they think will make them happy, only to find that it's like the pot of gold at the end of the rainbow. When they get where they wanted to be, what they wanted isn't there any longer.
If there is a God, however, it might make a great deal of difference. It might be that you, and everyone you know, has an eternal life. Perhaps the day will come when the stars go out like lights, one by one, and you'll be watching.
So how do you know? If it's so important to decide whether God exists, why is it so hard? Why is God silent?
I believe there is a God. I believe he's not silent. He speaks loud and clear to those who believe. That's the price of admission: faith. It doesn't have to be a robust, mature faith at the start, but a sincere willingness to believe is usually rewarded with increasing confidence.
I believe that the essence of God is love. Love is incomplete without an object. God would not be incomplete, so he created us to receive his love. With our finite senses, and our material nature constantly contending against the spiritual, we aren't able to come to know God in our own strength; so he has reached out to us over and over again. His ultimate contact was in fleshly form, in the person of Jesus Christ. He walked on earth as a man, at a specific place and time in history, and the waves from that incarnation have spread and washed over the whole world.
My answer to the question, what do I want to do with my life, is a natural outcome of those beliefs. My purpose is to serve God, to glorify him, and to please him. I didn't make myself. I owe everything I have, everything I am, to God. I owe him my service. It's joy to serve him. He can use my service to bring about everlasting good. Anything I do that's not in God's service is sure to wither away and vanish.
Read the Bible. Pick a modern translation like the NIV (New International Version), RSV (Revised Standard Version), or Good News for Modern Man. Start out with the four gospels, Matthew, Mark, Luke, and John, which start about 3/4 of the way through the book (look for the beginning of the New Testament). If there's a Christian group where you live, they'll probably give you one free for the asking. You can also find the Bible online in various places. Project Gutenberg has several versions, including the complete King James. Gospelcom has this Bible page.
Join a Christian fellowship. None of the people you meet there will be free from flaws, but some of them will have enough experience in faith to be able to help you find your way.
Pray. Go into a quiet place by yourself, if possible. Say whatever you can with sincerity: "God, I really want to believe in you. Please help me. Send me someone who knows you, and let us start talking about you. I've followed my own way in the past. I've hurt myself and others. I'm sorry. I want to try your way now." Do it every day until something happens.
Read books by Christian writers. The Bible is authoritative for Christians, but we often need help to understand what it means in the present day. "Mere Christianity" by C.S. Lewis is one of my favorites. If you have trouble believing that Jesus was the son of God or came back to life after his crucifixion, read "The Case for Christ" by Lee Strobel (Zondervan). The Christian Classics Ethereal Library is a fantastic collection of public-domain Christian writings from Saint Augustine to G.K. Chesterton.
Here are some other Web pages that might also help you.