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Am I right to assume that the question is about the other person's personal method of studying English? And would omitting the 是 make the question more general?
(Is this an example for the topic-comment structure: http://resources.allsetlearning.com/chinese/grammar/Topic-comment_sentences)
是的 constructs are for emphasizing.
你是怎么学习英语的？ = How did you learn English?
你是什么时候来的？ = When did you come here?
我是来看病的 = I have come to get a medical exam (as opposed to a social visit).
"是。。。的" is used to emphasizes the time, the place, the way (solution) of doing something or the agent who does the action. What is emphasized must be something that has already happened. So basically in this question "你是怎么学习英语的？" the person who said it wanted to know exactly the method of studying that the person was mentioned (你) had used. When omitting this structure the question will be: "你怎么学习英语？"， the action “学习英语” does not be emphasized and it might has not happened yet. I think the difference between this two are just the matter of tense.
