"How is your studies?" "How are your studies?" "How is your study?" Which one is correct among the three?
At least in American English, the only one of these that is correct is "how are your studies." The other ones are either grammatically incorrect or not really consistent with the ways in which Americans use the language.
First of all, "how is your studies" does not work grammatically. The word "is" is used with singular nouns. But the word "studies" is a plural noun. So these do not agree with one another.
You could then say "how is your study" because "study" is a singluar noun. However, Americans do not refer to a person's study (except perhaps as a room -- you might have a room called a study). If you are talking about such a room, this is okay, but in terms of what you do in school, we do not talk about your study.
"How is your studies?" is not grammatically correct. Studies is a plural noun and is is a third-person singular verb, so the sentence lacks subject-verb agreement. I understand the misunderstanding in this particular case, since the writer might mean that studies are a single concept. For example, "How are you doing in your Spanish studies?" implies a single subject. Nevertheless, the rule still applies for the reasons I just gave.
"How is your study?" implies that the speaker is asking how a room of your house is doing.
"How are your studies?" uses correct subject-verb agreement, since are is a third-person plural verb. This is the best choice.