How did the Black Plague come to an end?

Slowly built up immunities in the populations exposed. The people who didn't die in the first wave had some resistance-either genetic or environmental through better food etc, and the genetic resistance was ped on. It took several hundred years to finally stop-each generation faced an outbreak, usually the weak died off (children and old people) while the fit and relatively healthy were less affected. Improvements in hygiene helped too.