1) You told the world you were the father. Sounds strange, but the reality is that you could become the legal father if a man "receives the child into his home and openly holds the child out as his own natural child." This is father by "conduct and words."
2) You made an attempt to marry the mother before the child was born and the child was born within 300 days of the ending of cohabitation. The law is not so clear on what an "attempted marriage" is and how you need to fumble the ball, but an attempt could be good enough. You must have lived with the mother, attempted to marry the mother and have the child born within 300 days of moving out. The idea is that just because some technicality, or tornado or other crazy event kept the marriage from being formalized should not stop the law from "presuming" who the father is.
3) You're married. Even if you are not the biological father, the law presumes you are the father if the child was born while you were married to the mother. Yes, the law presumes faithfulness and biology.