How serious and common is dilated cardiomyopathy?

Depends. It is not that common but can be caused by various reasons including childbirth, infection or drugs to name the most common. In most cases patients recover or can be treated by medications. Make sure you find a good doctor who specializes in this.
Fairly common. Unfortunately it is becoming more common. It can be mild or severe with associated heart failure. Treatment is tailored to the underling cause.