Bergamot is a perennial herb, grown to make tea. I'm not keen on herb tea so I have to admit that I've never used it. I do grow it however, so if you like herb tea, here's how it's done.
Plant bergamot in rich, moist soil, in full sun. Keep the soil moist until well established and that's about all you have to do.
Propagation is easy. Either divide the clump to create more plants, or remove stems from the base of the plant making sure there is some root attached and plant on.