Well, it depends on which elements of Elizabethan audience you're referring to. If you're talking about a sophisticated theater going audience-- remember this was a time when the theater was very much alive-- they would respond in many ways like a sophisticated theater going audience today. That is to say, they'd be likely to compare it to other "special effects" from Shakespeare's other plays, or from other period plays. If the play were done in the country, though, there would be likely to be more fear-- more treating it like it was real.
However, that said, they'd have been more likely to accept that the ghost was back and important than modern audiences; there was a strong belief in ghosts during the period. They'd also be more likely to expect the ghost to be important in the plot than a modern audience-- to have and communicate more specifics about their death and the nature of the afterlife.