Please assist me with some pointers to get started on my essay. I am to discuss/argue the concept and use of the Byronic Hero in Wuthering Heights.

First of all, you need to establish what a Byronic hero is. Usually, a Byronic hero is defined as a deeply flawed character, isolated from society, a true individual unconstrained by any human laws or conventions. In relation to Wuthering Heights you're naturally going to be looking at the character of Heathcliff. He is generally thought by most critics and scholars to be a prime example of the Byronic hero. At the same time, it's important to recognize just how closely Heathcliff's identity is bound up with Catherine's. So in that sense there is a subtle difference between Heathcliff and other Byronic heroes such as Manfred; he is isolated but not completely.
In fact, you could reasonably argue that Catherine is also a Byronic hero to a certain extent. She, like Heathcliff, goes against established traditions and conventions. In writing your essay you may want to explore the possibility of treating Heathcliff and Catherine as two parts of a heroic Byronic whole. In particular, you might like to examine the similarities between the two characters and then set out to provide examples from the text that support your argument.
Good luck with your essay.