Being a very religious society a lot of the prevention effects involved praying and public displays of penitent and famous example would be the Flagellants who publically whipped themselves, their popularity soared during the time of the black death. There is no evidence that any religious practice was successful so I'll move on.
There were a lot of 'plague cures' going around. One that involved tying a live chicken to a bubo (plague swelling) and others that involved drinking potions of mercury. A big theory at the time was that the plague was spread via bad air or misama which is why plague doctors developed a long beak-like protrusion on the front of their mask, which was filled with herbs and spices. A lot of common folk carried around a pomander a vessel of sweet smelling substances, designed to keep misama away. Naturally none of those methods worked due to a misunderstanding of how diseases spread.
One other method to prevent plague was to attack minority groups such as the Jews, lepers and just general foreigners who were blamed for the plague and subsequently attacked. Famously at Strasbourg were over 2,000 jews were killed for their apparent involvement in spreading the plague. This also wasn't effective.
Methods that did work were: Quarantining ships, most famously in Venice, where ships had to wait 40 days to enter the city to make sure that there was no spread a lot of coastal cities boasted a Lazaretto; an island for quarantined sailors. Venice also use their Lazaretto to bury plague victims. Houses were also sealed up with the occupants inside if they were suspected of having plague. Milan avoided a major plague outbreak by relocating them to a pesthouse outside the city walls which might be the best example of a city avoiding a major outbreak. Venice did eventually fall to the plague.