Find mossy cobblestone in dungeons, jungle temples, igloo basements, and trail ruins
Mine mossy cobblestone with any pickaxe
Craft mossy cobblestone using 1 cobblestone and 1 vine
Use a stonecutter with cobblestone and moss block, if available in your version/mods
Trade with wandering traders or other villagers if your version or server supports it
Generate it naturally in certain structures and mine it there