Mostly, people ran away. Those who could afford to settled in pastoral settings and hoped it would pass them by. Since the plague spread rapidly and killed animals as well as people, this didn't always work so well.
Doctors advised burning aromatic substances to purify the air. They also used bleeding, purging with enemas or laxatives, hot plasters and lancing the swellings. Medicines were made of stag horn, rare spices, myrrh, saffron, and powdered pearls or gold (apparently on the theory that the more expensive the ingredients the better the effect). Floors were sprinkled with vinegar and rosewater, and people were advised to wash their hands and mouths with the same. Mild exercise, bland diets, and avoiding anger or excitement, especially at bedtime were prescribed. None of these worked at all, except that Pope Clement VI was ordered to sit between two large fires in his apartments during the summer. That probably did work, since the heat apparently kept fleas away.
Although medicine was far more advanced at the time than we usually realize today, doctors had no idea of germs and believed astrology and the humors (sanguine, phlegmatic, choleric and melancholic) were responsible for all human activities. The "scientific" explanation of the time was that the disease was caused by a triple alignment of Saturn, Jupiter and Mars in Aquarius.
There were several things done to try and cure the citizens of the plague. The doctors often “applied violent drawing–plasters or poultices to break tumors, and if these did not do they cut and scarified them in a terrible manner.”
Some were able to obtain “anti–pestilential pills” to help with the infection. The people were also encouraged to make sure the sick person remained clean and especially clean the sores, and tumors. Another method used was to “bleed” the patient to try and cleanse the body of infection.