‘We are talking of something entirely different, not of self-improvement, but of the cessation of the self’
Seeing there is no self (ie. no doer, no independent entity that is the author of thoughts and actions) is ‘cessation of the self’.
It is not something you have to do – that would be more self-improvement.
With this insight suffering falls away by itself, as a side-effect. Not that it matters, for there is no choice, just spontaneous happening.