It is important to know that limited slip differentials come in different sizes. Before buying a new unit, you must identify the rear housing. The primary concern is the number of splines on the axle. They should be 27 or 32, but depending on your vehicle this could be more or less; at any rate, the exact number is needed. The size of the opening for the differential---8.25, 8.50, 8.75, etc.---should be given. You also need to know how many bolts are in the cover. It could be a 10- or 12-bolt rear.
Raise and support the rear of the vehicle on jack stands. Move the gear shift to neutral.
Using a wrench, remove the bolts in the driveshaft yoke where it attaches to the pinion shaft. Lower the end of the driveshaft, but do not pull it out of the transmission.
Detach the wheel/tire assembly using the ½-inch drive air gun and a socket. Remove the rear brake drums. Place the drip pan under the differential cover, and remove the cover bolts with a 13 mm socket.
Remove the cover slowly to allow the oil to drain into the pan. Use the common screwdriver to pry the cover loose. Turn the differential by the outer axle hubs so that the center pinion gear retaining pin end with the small retaining bolt is facing you and slanted down enough so that it is just clear of the edge of the housing. Remove the small retaining bolt with a small wrench.
Pull the center pinion pin down and out of the carrier, remembering not to move the differential carrier with the pin out. If it is moved, the pinion gears will slide out of position or fall out. There is a special procedure just to reinstall the pinion gears and their bushings and line them up with their holes.
Push both axles all the way in toward the center of the vehicle. Remove the C clips from the inside ends of the axles. The clips keep the axles from coming out of the differential. Once they are out, pull the axles halfway out of their respective tubes.
Install the center pin carefully to keep the pinion gears from moving. Screw in the retaining bolt loosely. Remove the two vertical retaining caps on either side of the differential carrier, using the ½-inch drive air gun and a socket.
Pull the differential out carefully (it's heavy), and lay it on a clean cloth. Be careful not to mix the two spacers on either side of the carrier. They must be installed on the same side since they are of different thickness. The same applies for the bearing races---they have individual wear patterns.
Stand the carrier up on end, with the ring gear down and the retaining bolts up. Pull out the bolts from the back of the ring gear, and remove the ring gear. Place the new differential in the center of the ring gear, then lift the gear up to meet the new carrier. Install and tighten the retaining bolts in the ring gear.
Install the new differential carrier, with the bearing races on the bearings and the spacers installed between the bearings and the housing. Attach the vertical retaining caps over the bearings on the carrier, and tighten the bolts.
Turn the differential carrier again so that the center pinion pin is in position to drop out when the retaining bolt is removed. Remove the bolt and drop the pin out. Push both axles all the way in toward the center of the vehicle. You may need to move them around enough to align the splines on the end of the axle with the splines in the carrier. Install the C clips on the inside end of the axles and then pull the axle all the way out as far as it can go. This moves the C clips into a pocket from which they cannot fall out.
Install the center pin and its retaining bolt, and tighten. Scrape and clean all dirt and gasket material from the differential cover. Smear a thin, continuous layer of silicone sealant around the entire cover, and allow it to dry for 10 minutes. Line up the differential cover, then insert and tighten the bolts.
Remove the filler plug on the differential with a wrench, and pour in the limited slip additive and oil until it begins to run out of the filler hole. Attach the filler plug and tighten. Then install the remainder of the parts in reverse order of removal.
