We have already talked about the basics of star formation. The fundamental ideas are:
At this point, the cloud becomes a star and assumes its place on the Main Sequence
To make the ideas concrete, I will talk about the formation of stars of mass, say, less than around 2 x the mass of the Sun. Such protostars are referred to as T Tauri stars. Note, however, that the basic ideas are the same for all protostars. It turns out that it is primarily how protostars appear and where they form in the clouds (and therefore presumably how they are triggered) which differs according to their masses.