If you keep in mind the rule concerning subject verb agreement the correct sentence is "How are your studies?" The rule states that the subject and verb must agree. If you have a plural verb, you must have a plural subject. If you have a singular verb the subject must also be singular. Subjects and verbs must also follow parallel structure and be the same tense throughout the sentence.
Also keep in mind that the statement, "How are your studies?" is not a correct formal sentence. This is a question that is worded rather awkwardly. A better way to write the sentence would be, "How are you doing with your school work?"