Here's a breakdown:
* Murderer: Claudius, Hamlet's brother
* Method: Poison poured into the ear while sleeping (implied, not directly stated)
* Circumstance: The murder happened while Hamlet's father was sleeping in the garden, leaving him vulnerable to the attack.
The ghost's revelation is key to the play's plot. It fuels Hamlet's thirst for revenge, driving him to act (or rather, not act) in a way that ultimately leads to tragedy.