1) look under your car, see if there is a tag hanging off the diff oil filler plug saying "LSD: USE APPROVED LUBRICANT ONLY"
2) do a burnout and see if you leave 2 black lines.
3) jack up both back wheels, put it into neutral, turn one wheel and see if the other wheel turns the same way (LSD) or if it turns the opposite way (single spinner).
note that with the above method, if your LSD is completely buggered it will act like a single spinner.