There are more tactical explanations in chapters "connecting stones" and "capturing stones". It is usually good idea to play many capture go games before reading tactical advices.
In following problems you need to identify last remaining place, where points could be gained, or reduced. The gained points are marked in the correct answer. The lost reduction opportunities are marked in wrong variations.
In the end black cannot reduce white liberties to one, and the ladder fails. The result is bad for black. Blacks stones are weak, and no white stone is captured. White can expect to attack or capture some of the black stones.
White cannot play to A, because white stone would not have liberties. Also white cannot play to B, because again white stone would not have liberties. So white cannot start killing at all.