A man want to quit smoking.

Sorry I made a spelling mistake.
The title shuld have been "A man wanted to quit smoking."

Any my question is that "What the specific meanings of these methods?especially the last two."

Now 69 people have viewed my question. Who can answer me? Patience is a virtue, I am still waiting for you.

tapering off means smoking less over time until you quit
the buddy system is having a friend quit with you for support
relaxation exercises could be many things, meditation, controlled breathing
affirmations refers to positive suggestions either thought, spoken or maybe written down as little notes, something like "you can do this", "one day at a time"

What means by his methods?

This is not idiomatic English, Nancy. When we ask in this fashion we use either,

What does [____] mean? // What do [__] and [__] mean?

What is meant by [__]?