What plan does Hamlet come up with so that he can determine whether the Ghost he sees in act 1 is the actual ghost of his father or that of the devil?

At first, Hamlet is unsure whether the Ghost is really his father or just some malevolent demon trying to trick him into committing murder. Hamlet wants to make absolutely certain of the Ghost's true identity before he decides to set about killing Claudius. Hamlet has good reason to be cautious; murder is a serious business, especially if it involves a king.

May be the devil, and the devil hath power T' assume a pleasing shape. Yea, and perhaps Out of my weakness and my melancholy, As he is very potent with such spirits, Abuses me to damn me. I’ll have grounds More relative than this. The play’s the thing Wherein I’ll catch the conscience of the king. (Act II, Scene II).

So Hamlet hits upon an ingenious scheme to test the veracity of what the Ghost has said. He's going to stage a play called The Murder of Gonzago. The play will be a realistic one, heavily rewritten by Hamlet himself to depict the events of his father's murder as related to him by the Ghost. As the play unfolds he's going to watch Claudius like a hawk to see his reaction. If, as Hamlet suspects, Claudius really did murder his father, then his wicked uncle will squirm uncomfortably as the extraordinary depths of his evil are exposed on stage for all to see.