The way that he incites the riot is by disrupting the distribution of soma to the deltas at the hospital. They are all looking forward to their dose and are outraged when he starts to throw it away
The reason why he does it is that he does not think that people should drug themselves to the point where they have no feelings. John is upset because his mother has just died and no one is acting as if it matters. He feels that it is terrible to live a life where you don't even care about someone dying.
The Savage is grief-stricken because Linda, his mother, has died. As he leaves the Park Lane Hospital for the Dying, he finds himself in the midst of a group of Deltas ending their work shift. He finds himself surrounded by a sea of two types of identical faces, all waiting for their soma ration.
As he gazes at these identical faces, the words "O brave new world!," spoken by Miranda in Shakespeare's The Tempest, occur over and over to him ironically, for this "new" world is anything but brave or glorious. The words "mock" him.
But all of sudden, the meaning of the words change for him. He realizes that Miranda in The Tempest was uttering a call for "loveliness, the possibility of transforming even the nightmare into something fine and noble." The words "brave new world" suddenly turn into a challenge and a command to him to act.
The Savage thinks with grief that his mother died "a slave," lost in a soma-induced stupor, but that others, like the deltas all around him, could live free. This world could be made free and beautiful. "Suddenly it was luminously clear to the Savage what he must do."
At that moment, he decides to disrupt the soma distribution. He begins to throw away the soma, shouting to the deltas that they are "free." The deltas don't like this at all: they want their soma, not freedom. They begin to riot as the Savage tosses their soma out the window. The riot is quelled by policemen spraying soma vapor into the air and by the "Voice" of anti-riot tape II soothing the deltas.
John, the Savage, had not wanted to instigate a riot: he wanted to free the deltas from their mindless dependence on a mood-altering drug. He wanted to free them from their stupor, to offer them beauty and humanity. He offered them, truly and non-ironically, a "brave new world."