Just a couple of other points to Aineo's excellent response:
1. Jesus defines born of water in His discussion with Nicodemus:
"Flesh gives birth to flesh; but the Spirit gives birth to spirit." Water birth is physical birth. We are born when the bag of waters breaks. We can only be born of the Spirit because Christ Himself was broken for us.
2. In Romans 6:3, Paul makes it clear that the baptism of the believer is not a water baptism, but one into the death of Christ. We are IMMERSED into His death, and thus our old natures die. Those who desire water baptism do so as a matter of public testimony, not as a matter of salvation.