Your question really gets to the heart of what it means to be a Christian. To become a Christian means much more than just having our sins forgiven. It means a complete change, from opposing God and his rule over our life, to submitting ourselves to Jesus’ rule. Having our sins forgiven is only a part of that. It is an important part, because we could never be friends with God unless he forgave us, but it is still only a part.

The outcome of becoming a Christian is that we are now at peace with God, being his child again. Living as a Christian means living the way that God wants us to live. If a person persists in living in a way that doesn’t please God, they have either misunderstood what the Bible teaches on how to live, or they are still living as an enemy of God.

1 John 1:5-2:6 is a Bible passage which will hopefully be helpful to you. It explains that God is completely sinless, so whoever would have fellowship (be friends) with God must try to live God’s way, without sinning. It says that whoever claims to have fellowship with God and yet does not try to live God’s way is actually a liar. Having said that, it admits that it will be impossible for us to be completely without sin, so what we should do is confess our sin, knowing that Jesus Christ is the righteous one who died to pay the penalty for our sins so that we could be completely forgiven.

Colossians 3:1-17 and Romans chapter 6 are also good passages to look at. These explain that when a person becomes a Christian they should start living how God wants them to live, not how they used to live.

Also, check out:
http://www.christianity.net.au/you/what_should_i_do_now
and:
http://www.christianity.net.au/you/what_is_a_christian