How can I know the exact meaning of “cousin” in a sentence?

Your question is very unclear, but I suspect that you're wondering if English has a way to distinguish between any of these kinds of relationships:

• male cousin vs. female cousin
• cousin on your mother's side vs. cousin on your father's side
• child of your father's sister vs. child of your father's brother
• etc.

The answer is no. English uses the same word cousin for all of these relationships, and there is no single word that distinguishes between any of these combinations. If you really need to specify the gender, for example, you can say "male cousin" or (more informally) "boy cousin". If you want to specify whether you're related to a cousin through your mother or through your father, you say "cousin on my mother's side" or "cousin on my father's side".

Many other languages have separate words for at least some of these relationships, but English doesn't. English speakers get along just fine without special words for these relationships, and often find it very difficult to consistently make these distinctions when learning a foreign language.

English, as famous as it is for having a large vocabulary coming from a Germanic and Romance base and bolstered by a huge influx of Latin and Greek neologisms, is notoriously lacking in kinship terms. There is little distinction in terms of sex/ side of family, marriage relation,

So the answer to your question is there is no -easy- fluent way to translate exactly. You'd have to say in English 'my mother's sister's son' to specify the real family tree relation.

How can I know the exact meaning of "cousin" in a sentence? How do English speakers distinguish between different kinds of cousins?

How do you tell if a person being discussed is left handed or right handed? If you needed to know, the speaker should have told yuou.

If the usage and context doesn't provide you enough information to determine this, either the speaker made an error or the speaker didn't intend for you to have this information. Necessary information will be missing if speakers make errors. And, of course, there's no way to extract information from a sentence that the speaker chose not to put in there.