In the very first lecture of my Metaphysics class this semester, I told my students that I have no answer to the question "What is metaphysics?", that I won't give them any definition of "metaphysics" for the simple reason that I don't have one. They seemed surprised. To assure them that I am indeed qualified to teach metaphysics, I told them that I could tell them a lot of things about metaphysics, it's just that I don't think there is a definition of "metaphysics" that would cover all and only views or theories that are considered metaphysics.
My approach in this class is to introduce and discuss some standard metaphysical issues, such as personal identity, free will and determinism, and possibility and necessity, before we talk about what metaphysics is. My hope is that towards the end of the semester they will have a good sense of what metaphysics is without being given a definition of it.