The US government allows dual citizenship. If your home country allows you to maintain a second citizenship, you may be able to retain your original citizenship while enjoying all the privileges of US citizenship. The advantage of dual citizenship is that you do not have to give up close links to your home country. By having citizenship from both countries, you can also travel on either a US passport or on a passport from your home country. This can make it easier for you to travel back and forth between the two countries, especially if you plan to travel often to see family and friends back home.
However, there are some potential drawbacks to having dual citizenship. For example, you may need to pay taxes in your home country. If your home country has required military service, maintaining your citizenship may still commit you to this requirement. You will also need to obey the laws of both countries. In addition, the very highest levels of security clearance in the US typically require you to be completely free of foreign influence, so you will generally not qualify for this level of security clearance with a dual citizenship. However, for the vast majority of Americans, this level of security clearance is not necessary.
The first step in obtaining dual citizenship is to decide whether the advantages outweigh the disadvantages for you. The second step is to find out whether your home country does permit dual citizenship. If the country does not, you will be surrendering your native country citizenship when you become a US citizen through naturalization. You will want to be aware of this.
If you have considered carefully and your home country does permit dual citizenship, applying for dual citizenship is as simple as applying for US naturalization by filing Form N-400. When you become a US citizen, you will not give up your original citizenship (as long as your home country permits dual citizenship) and you will be both a US citizen and a citizen of your home country. You do not have to file a special form or request to enjoy US dual citizenship.