A couple of ways...
1) On the sticker on the driver's door jamb, there will be all sorts of information (VIN barcode, stock tire size, axle code, etc.). Find the axle code; it'll be two characters. Then refer to this page to decode it.
2) There should be a metal tag attached to the rear axle by one of the differential cover bolts, that will have the axle ratio on it, and also whether or not it's a limited slip. If it's a 3.73 limited slip, it'll have something like 3L73 on it.