This is an absolutely beautiful question that I come across quite often. If we try and understand the character of God throughout the Bible, we see that God's main purpose for us is to live in relationship with Him and each other. Jesus had said in Matthew 22, “You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself"
So what is our purpose? - These two commandments given above show us a very quick snapshot of our purpose and if you notice, these purposes are continuous - everyday is a new day to love God and everyday is a new day to love your neighbor which means there is no real end to our purpose.
Another important part of being a child of God is to spread His wonderful word. In Matthew 28 verse 16 onwards we see Jesus giving us the Great Commission, to spread the Gospel and make disciples of the world; to make sure everyone can experience the same joy and love that we experience with God. To do this, God uses our individual skills, strengths, weaknesses and friends/family/work circles.
The best way to learn more about God and His individual plans for us and to find out about our gifts is to join a Bible based, Spirit led church and/or Bible study group. Such groups also allow you to interact more with people from different backgrounds which helps us understand our God given gifts more as well which could lead to an even greater more specific purpose God has for us. He reveals all in different ways!