He began, as moral philosophers often do, with his own definition of human nature. Human beings are “under the governance of two sovereign masters, pain and pleasure”. He means that human beings are pleasure-pain organisms who will always seek out pleasure and avoid pain. For Bentham, laws should be passed only if they maximize pleasure and minimize pain for the majority of people.
This is how Utilitarianism works.
You then set about doing “happiness sums” with something Bentham called “felicific calculus”. (You ask how intense the happiness will be, how long it will last, how likely it is to occur, whether it has any unpleasant side-effects and so on.) You also try to ensure that the happiness is spread as widely as possible, so as to produce what Bentham called “The General Good” or “the greatest happiness of the greatest number”.