Sentence/sightseeing

Method OF Learning is totally right, because here it's a noun.
You could also use FOR, but I don't see any reasons to change that.
But if your intention is using "learning" as a verb, like "I use this method to learn english",
You SHOULD change that for TO. You can use FOR if you change the phrase to:
"I use this method for english learning" because here it's a noun.

Wang Chun

It depends on the full context, these are possibilities from my angle:

Combining in balanced regiment of reading, listening, writing and speech exercise is the most affective method of learning English.

The most affective method of learning English is to practice a balanced regiment of reading, listening, writing and speech exercise.

Visiting / touring the United States gaves me an opportunity to immerse in an English speaking environment and to learn the American culture.