The dictionary says: A person with a high degree of skill in or knowledge of a certain subject.
Perhaps the question you meant to ask is, how do I tell whether or not a person is an expert?
Here's my personal answer.
1) I regard someone as an expert if they can show me that they can accurately convey detailed information on a topic directly from memory, and when needed can remember or quickly rediscover the source from which they that got that information. Think of a lawyer who cites a legal decision, or a minister who can literally "cite chapter and verse."
2) Someone who has done so much valuable work on a topic that he is cited as a source by many others, either formally (in a print citation) or informally (someone telling you "go see so-and-so about that.")