The two most common ways a person obtains U.S. Citizenship are birth and naturalization.
Any person born in the United States subject to the jurisdiction of the United States is automatically a United States Citizen at birth. Also, a child born to one Citizen parent and one Non Citizen parent is a Citizen at birth if the Citizen parents has five years of residence in the United States and two of the five must be after his or her fourteenth birthday prior to the birth of the child. This has been the law since 1986. Prior to 1986, the rules vary from different periods of time.
Naturalization has more than one meaning and is defined under the Immigration and Nationality Act as the conferring of nationality of a state after birth by any means whatsoever. The most common type of Naturalization is when a person has a resident alien card for a number of years and then applies for Citizenship and takes an exam and passes that exam along with all of the requirements including good moral character. A person is given a Certificate of Naturalization and has all the rights of Citizenship except he or she cannot run for the office of the Presidency of the United States.
The other types of Naturalization occur when a parent becomes a United States Citizen and their child obtains derivative Citizenship. The derivative Citizen is given a Certificate of Citizenship. This type of Citizenship grants all of the same rights as Natural Born Citizens except the person cannot run for the office of the Presidency of the United States.
This is a general overview of U.S. Citizenship. For answers to your specific questions please set up a consultation with a Las Vegas immigration lawyer today.