"What year are you in?" Answer: "I'm a sophomore," or "I'm in my sophomore year."

Dan has answered your question very well. I'd just like to add the following information: In the US, a college (university) education usually takes four years to complete. The first-year students are called "freshmen" (singular: "freshman"), the second-year students are called "sophomores," the third-year students are called "juniors," and the fourth-year students are called "seniors." American high schools also usually offer a four-year program -- grades 9 to 12, and the same terms "freshmen" etc. are also used for the high school students.

Exactly. This language would only apply in the USA.

...an american college ... Not many other countries use that naming system.