United States allows foreign nationals to naturalize and become US citizens and the country also allows people to hold dual nationality. People who are citizens of foreign countries may become US citizens and they may not be required to give up their current nationality. Citizenship laws differ from country to country and some countries do not allow the citizens to hold dual citizenship. However, a US citizen who voluntarily becomes a citizen of a foreign country will be stripped off his US citizenship.
A US citizen may become a citizen of a foreign country if he/she gets married to a citizen of that foreign country and such US citizens who automatically become citizens of foreign countries will not lose US citizenship. Similarly, a person who applies for naturalization and becomes a citizen of the United States, need not forsake his country of origin. Citizenship laws of America do not require a person to give up his citizenship to obtain US citizenship. Such a foreign national may become a US citizen and remain a citizen of his home country. US citizens who automatically become citizens of other foreign countries may not lose their US citizenship, but US citizens who willfully apply for foreign citizenship and who intend to relinquish US citizenship, are likely to lose US citizenship.
Dual nationals must follow the laws of both the countries and both the countries will enforce their laws. Dual nationals must use the passports issued by the United States to travel to the United States and they must use the passports issued by the other foreign country to travel to that foreign country. However, you need to remember that there are few countries that require people to choose one citizenship or another and such foreign countries will take away your citizenship after you become a US citizen. Nevertheless, you need not forsake your home country to become a US citizen.