How do you get custody when child's parents are not married?

Answer 1

An unmarried father must establish his paternity and arrange for a custody hearing if he wants custody.

Generally, if the parents are unmarried the mother has sole custody and control in most states until the father can establish his paternity. Remember, a child's mother can always be identified by medical records. Since the father didn't give birth and he was not legally married at the time of the birth he must establish his paternity by signing the birth certificate at the time of birth (waiving DNA testing rights) which must be done with mother's consent. If he doesn't sign the birth certificate then he must seek another way to establish his paternity and that is done through a DNA test.

A paternity test can be arranged through the court. Once paternity has been established the father can request visitations, joint custody, full custody or the court will set up a schedule of regular child support payments for the child if she is to remain in the custody of her mother.

Answer 2

There really is no way that I am aware of to get visitation if you are not related. If there was, any stranger could take parents to court to try to see children. Even grandparents, in some states, have a hard time getting visitation.
For custody, there has to be a very good reason as to why the parents should not have full custody. Good reasons include; neglect, drug abuse, child endangerment, etc.... But even still, the court system would look for a relative to raise the child.