First, it should be "what" is the right way to say, not "how."
And for your sentence, I'd say it's incorrect to use "like." The only option here is "as" because the sentence by extension would be "I want to learn English as a native does" or "I want to learn English as a native learns English." Now, if you're talking about SPEAKING as well as a native, then that's a different story. But to say "like," as mentioned, is incorrect because you cannot compare English with such a preposition to a person--they simply have nothing in common. On the other hand, something like 90% of native English speakers use "like" incorrectly (according to grammar rules).