Parsing grammar of 你是怎么学习汉语的？ To my knowledge 是 means "is" and the usage of 的 that I am familiar with is that it is like a possession particle. I don't understand how either character functions in the following sentence:

你是怎么学习汉语的？
Nǐ shì zěnme xuéxí hànyǔ de?
How do you study Chinese?


If I took a blind stab at translating the English to Chinese, I would have went with something like 

你怎么学习汉语？


Is this attempt incorrect?

How do I understand the grammar of the original Chinese sentence?
This is one of those questions that a native speaker with a sound grammatical knowledge might be able to answer better, but from my point of view (as a native speaker with little grammatical knowledge), I think the best way to explain would be to show what the difference is to the listener.

As you may or may not know, the particle 是 is not always necessary from a grammatical perspective, especially when there is no ambiguity around the various components of the sentence, so grammatically both 

你是怎么学习汉语的？AND 你怎么学习汉语？are fine.

If someone asked you 你是怎么学习汉语的？(i.e. you are not reading this sentence from a page of a book), then it is more likely that they are putting an emphasis on the process in which you have managed to learn/acquire the language.

However, 你怎么学习汉语？can mean one of two things:


How do you study Chinese? OR
How come you study Chinese? (as opposed to studying Japanese)


In fact, 你是怎么学习汉语的？can also have this second meaning, but this would fall into the category of a very awkward way of asking this question, which is more natural without the 是 if you want to imply this meaning.

The only way to be certain is to ascertain the exact context of the sentence/conversation (as is often the case with some Asian languages). 

Example sentences:

有很多不同的语言, 你怎么学习汉语的？
There are many different languages, how come you study Chinese?

有很多不同的语言, 你是怎么学习汉语的？
Probably should be using 为什么 instead of 怎么 when accompanied by 是

你说的很流利, 你是怎么学习汉语的？
You speak fluently, how do you study Chinese?