Ghosts do not do much, they walk around the lot looking to scare the living. If a living Sim does happen to see one, you'll notice a scare icon on in the list of actions. Hauntings are possible even if the dead is not from the present family.
If you want to see a sim ghost without killing one of your Sims, check out the Goth house, a default family. The house has a graveyard, and most nights that I've played I had a haunting.
