The ghosts generally appear as semi-translucent versions of themselves, complete with the injuries they died by. There can be as much variation as you like, though, providing the ghost is capable of communicating clearly and doing some sort of harm to the character interacting with them.

Some of the spirits will take other fruits or foods, but some will only accept oranges. Generally, the more old-fashioned the ghost looks, the more likely they are to accept any fruit - old-timey ghosts are used to fruit being rare and valuable so will be more excited for anything; more recent ghosts are specifically expecting oranges as they know what this tradition is.