I'm still in university, but the vast majority of the work I get is through someone I know, not jobs I apply for. I would start putting the word out to anyone you know in the industry that you are looking for work. (Obviously, you should apply for jobs too, even if you don't know anyone in the company.)
In your case, your degree sounds like a general theatre degree. Something that helped me get comfortable working in the theatre (before I started university) was volunteering wherever I could -- community to large regional theatres. I met a lot of people that work in the industry (yes, even in community theatre) and some of them got me work later on.
I am sure that those who have been in the industry longer than me (which is almost everyone) may have a different perspective, but that is what I found as a student.