difference between method, manner, and way

method - a way of doing something, especially one that is well known and often used: You can choose whichever method of payment you prefer

way - a set of actions that you use in order to do something. Way is more informal than method and is used more often in everything English

manner - [singular] formal the way in which something is done or happens: In everyday English, people usually say in a ... way rather than in a ... manner

some explain of people:

• Approach, method and way can refer to how you set about/ start a certain task. The manner in which something is done.
  Way and method can also refer more to an actual fixed procedure, often according to a definite established, logical or systematic plan. 'There are three methods/ ways to cook an egg.'
  Means often refers more to what you use. The medium or instrument used to obtain a result.
  They are all very close in meaning but there is a slight difference.

• When words share the same meaning, you may use them interchangeably in your sentence, like for "example" and for "instance".. just be creative and play with vocabulary to enrich your language skills.

• They are synonyms.
  This is the way to go (road, route). This is the way to get that job done. Do it this way.
  We have a method we follow to fabricate this object. Our method is different from the way other companies do it.
  A method could be a prescribed procedure that is followed.
  The word "manner" is common, but we might not use this word as much. It means "way"
  English has many words that mean the same thing, and many are interchangeable. You would not be wrong to use any of these words.