How does the inspector teach Gerald and the Birlings social responsibility?

The Inspector teaches Gerald Croft and the Birlings that being wealthy and privileged doesn't entitle them to treat the so-called lower classes like dirt. Yet that's precisely how they did treat poor old Eva Smith. At no point did they regard her as anything vaguely resembling a human being. To them, she was just one of many working-class women that people like themselves have been exploiting for centuries in one way or another. She was expendable, existing purely and solely to serve their own selfish needs, before being casually discarded like a used handkerchief when she was no longer of any use.
Inspector Goole hopes through his unusual investigation to change this attitude of corrosive snobbery. He wants the likes of Gerald and the Billings to recognize that they have a social responsibility towards the poor and dispossessed. He does this chiefly by showing them the tragic consequences of their actions, something they will never have seen before at any time during their lives of pampered leisure. By individualizing the suffering and torment that Eva endured, Goole is speaking the language of the upper-class, the better to drive home his powerful message.
For it's perfectly clear that the likes of Gerald Croft and the Billings have no real understanding of society as a whole; they can only relate to other people as individuals. So it is at the individual level that Inspector Goole endeavors to spell out in full the consequences of their selfish actions.

When Inspector Goole enters the Birling home, he states that his purpose for being there is to question all those present, hoping to obtain information about a young woman, Eva Smith (also known as Daisy Renton), who killed herself by drinking disinfectant.
Initially, Croft and the Birlings don't understand what his investigation has to do with them, but as he questions each person, he exposes how their actions contributed to Eva's death.
Because the group knows at the outset that Eva died by suicide, the belief that it is too late to rectify the situation increases their sense of guilt and makes their self-reflection more poignant.
The inspector reminds them that everyone has a responsibility to care for those around them. While Mr. Birling remains skeptical of the inspector's words, the younger members of the party are determined to change.