Often times, when two kanji come together to form a kanji compound (or jukugo), you use the on'yomi readings. This is similar to that, though instead of another kanji it's a foreign word. This pattern works with almost any country as well. Just add 人 to a country name and you've described the people who live there. You'll see more of these before you're finished here.
And since 人 has two on'yomi readings, here's a mnemonic to help you remember which one to use:
Americans absolutely love their jeans (じん), it's a well-known fact!
Am I American?
There are two American people.
I made friends with an American girl.