If people work together on the same thing, they're working on a joint project. They're doing something collaborative.

共同 is used when two or more people or groups do something together with a shared purpose or responsibility. 共同作業 (collaborative work) means you share tasks with others, for example, and 共同生活 (shared living) means living together with someone, whether it's a partner or a roommate.

This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.