There are four fundamental ways to obtain U.S. citizenship:
- Birth in the U.S. or its territories
- Naturalization (obtaining citizenship after an application and exam)
- Derivation of citizenship (naturalization of one's parents)
- Acquisition of citizenship (birth to U.S. citizen parents)
In some circumstances, a child automatically "acquires" citizenship even though that child was born outside the United States. At least one parent needs to be a U.S. citizen at the time of the child's birth and several other conditions must be met. When this child marries and has children, those children may also acquire U.S. citizenship at birth.
The laws have changed several times over the years. You'll need to research the law that was in effect on the date of the child's birth (and the parents' birth, if grandparents were U.S. citizens).
Therefore, it is generally recommended that you seek the assistance of an experienced immigration attorney that can guide you through this process.