How did jesuits spread catholic faith among the masses?

The Jesuits, to paraphrase Star Trek, went boldly where no European had gone before.

The basic strategy of the Jesuits was to convert people who had never heard of Christianity. So, off they went into the world. Jesuits traveled throughout India and Japan and throughout Southeast Asia and Canada and converted along the way (with quite a bit of resistance from the locals).

they died because of a disease during the first spanish colonies.