Christianity, not surprisingly, is an ongoing thing. It's not like we convert and suddenly we become Jesus. When we become Christians, we continue to sin, not because we want to, but because it is just human nature. It's inevitable.
But because of the Spirit we are of, it should be a secondary, and very much unwelcome nature. Sin should be followed by confession, further followed by a desire to avoid it. But again, sin is just in our nature. We may want to avoid sin, but we will never truly succeed, at least not in this life. And so we rely on Christ. The key is to seek to be like Him, and rely on Him to make up for our failures to do so.
By this, we know that we are truly saved. False converts do not truly care. They act as if they are without sin, or as if their sin is no big deal. But as Christians, even knowing Christ is our advocate for our failures, those failures should still cause us grief. Strive hard for perfection, even knowing now is not the time to achieve it. This is how we prove our faith, to the world, to ourselves and to the Lord.