First, I don't know Hamlet. I'm quite familiar with Freud's theory of the Oedipus complex.
On wikipedia I found this:
Since the birth of psychoanalysis in the late 19th century, Hamlet has been the source of such studies, notably by Sigmund Freud, Ernest Jones, and Jacques Lacan, which have influenced theatrical productions.
In his The Interpretation of Dreams (1900), Freud's analysis starts from the premise that "the play is built up on Hamlet's hesitations over fulfilling the task of revenge that is assigned to him; but its text offers no reasons or motives for these hesitations". After reviewing various literary theories, Freud concludes that Hamlet has an "Oedipal desire for his mother and the subsequent guilt [is] preventing him from murdering the man [Claudius] who has done what he unconsciously wanted to do". Confronted with his repressed desires, Hamlet realises that "he himself is literally no better than the sinner whom he is to punish". Freud suggests that Hamlet's apparent "distaste for sexuality"—articulated in his "nunnery" conversation with Ophelia—accords with this interpretation. [...]
As far as the theorie of the Oedipus complex is clear to, you can start looking at Hamlet's behavior in order to find examples that back up the idea of the complex.
First of all, you are supposed to have a clear and brief concept of the theory as this acts as a basis of your paper.
Interested in Language