Many authors, especially African-American writers such as Alex Haley and Langston Hughes, have used their works to discuss what it truly means to be an American during their lifetimes. Think about this issue and what it means in your own life. In an essay using details from your own life experiences, explain what you feel makes a person an American. How can I start an expository essay on this topic?

How you will approach this question depends to a great degree on your own background and personal experience. A white, heterosexual male whose parents arrived in the US in the eighteenth century will often have a different viewpoint than a second-generation Asian-American woman or a gay Latina first-generation immigrant. The recent attempts by President Trump to ban Muslims from traveling to the US might affect how a follower of Islam would respond to this question.
Your first step would be to talk about the actual legal nature of US citizenship. If you were born on US soil or your parents are US citizens at the time of your birth, you are automatically a US citizen. If you were not a citizen at birth, you must apply for derived citizenship or naturalization. 
On the next level, one can talk about the history of the United States. Long before the Europeans arrived in the US, many Native Americans lived here and had complex and sophisticated civilizations. In an important sense, people of European descent are all foreign immigrants. Moreover, immigration into the United States came in many periods, types, and forms. For example, many people of Spanish descent lived in the Southwestern United States before that region actually became part of the US. 
For some people, the concept of being "American" will be focused on how long their families have lived in the US and for others it will be a deliberately chosen identity. Some people whose families have lived in the US for many generations may feel ideologically alienated or dispossessed in some way. 
The important issue in completing this assignment successfully will be to display an understanding of the diversity of the American population and realize that those diverse experiences and backgrounds lead to many different views about what constitutes being American. Your own position is just one of many possibilities.