There have been several polite terms used in the US to refer to persons of African descent: “colored,” “negro,” “Black,” “Afro-American,” and “African American.” “Colored” is definitely dated, though “people of color” is now widely used with a broader meaning, including anyone with non-European ancestry, sometimes even when their skin is not discernibly darker than that of a typical European. A few contemporary writers like to defy convention by referring to themselves as “negro.” “Black,” formerly a proudly assertive label claimed by young radicals in the 1960s, is now seen by some people as a racist insult. Some people insist on capitalizing “Black,” but others prefer “black.” The safest and most common neutral term is “African American,” but Americans sometimes misuse it to label people of African descent living in other countries or even actual Africans. To qualify as an “African American” you have to be an American.
Although it is traditional to hyphenate “African-American,” “Irish-American,” “Cuban-American,” etc., there is a recent trend toward omitting the hyphen, possibly in reaction to the belittling phrase “hyphenated Americans.” However, some styles still call for the hyphen when the phrase is used adjectivally, so that you might be an African American who enjoys African-American writers. Omitting the hyphen may puzzle some readers, but it’s not likely to offend anyone.