If you know that you still have the factory installed gear ratio, then you can look up the axle code that is on the sticker on the door jamb. Or, you can look at the tag that should be bolted to the rear diff. 2nd row starts with a number such as 3 73, which would indicate a 3.73 gear ratio. If there's an L where the decimal would be (3L73), then that axle came with a trac-lock clutch type limited slip. Front axle will have the same gear ratio as the rear, will always be open (unless aftermarket stuff has been added), and will be a Dana 35 TTB.
If you can't be certain that you still have the factory installed option, then you will have to actually "count" the gear ratio. Rotate the tires through one rotation while counting the number of rotations of the driveshaft. The number of rotations of the driveshaft per rotation of the tires is the gear ratio.
You can check for a limited slip by measuring the torque required to rotate one tire while the other stays still. This only works if you can assume the clutches are still good (Probably not a good assumption unless you know for sure that someone has checked the clutches). The surest way to know if you have an LSD installed is probably to open the rear diff and check visually.