I suspect you’d be disappointed if the answer to this question was clear-cut and easy. Like so much in immigration law, the answer “depends.” Here are some basic guidelines for this question – but keep in mind that this is only a starting point.
What’s good is that since the passage of Child Citizenship Act (CCA) in 2000, the rules have actually been simplified. The current rule is that if your child was born abroad to at least one U.S. citizen parent, she will automatically receive U.S. citizenship when all of the following requirements are met:
Your child is under 18 years old;
Your child is either admitted to the U.S. as a permanent resident or receives this status through the process of “adjustment of status”;
Your child is permanently residing in the U.S. with you, the U.S. citizen.
However, if you and your child reside outside the U.S., then your child will not automatically receive citizenship. You will have to formally submit an application for naturalization for your child and also meet other requirements. In particular:
The U.S. citizen parent must have lived within the U.S. for at least five years (this can be cumulative – broken up by trips abroad – and doesn’t have to be a continuous five years);
The U.S. citizen parent must have lived at least two of those five years in the U.S. before the U.S. citizen parent’s fourteenth birthday;
Your child must be under the age of 18;
Your child will need to be in the U.S. to complete the naturalizatio process and recite the oath of allegiance (unless the child is very young, and then the oath can be waived).
Overall, these rules have changed frequently and note that the law at the time of your child’s birth will be what applies to her regarding citizenship. So be sure to research what the current rules are or consult with an attorney whenever your child is born.