The usual expressions are: give up smoking quit smoking 'Cease smoking' is rather too formal for everyday use, though it could be used in a medical/healthcare context. The noun 'cessation' is also used by healthcare professionals.

Which phrase you use will depend on what you mean. If you mean to break the habit of smoking tobacco, you can use the following phrases. I quit smoking last year. I want to stop smoking/ I want to quit smoking. You would not normally use cease in this context of stopping a tobacco habit. If you said he ceased to smoke, it would sound awkward. It sounds like he might have been on fire or something. Also you would not say 'I stopped to smoke.' This would be interpreted to mean that you stopped doing something so you could smoke a cigarette. The best way is with the gerund - I stopped smoking. There's an old joke based on this. When I drove a taxi many years ago, some customers would ask me if it was ok to smoke in the car. They would say, "Do you mind if I smoke." The joke answer was, "No, I don;t mind, you can burn for all I care." So when we say something like I'm smoking, if taken literally, it means my body is making smoke, probably because my clothes are on fire. (haha, it's not really that funny as a joke.)

give up smoking

You can say : I don't smoke anymore

Quit 'er'