I use 2 hydraulic floor jacks for this process. (Some people use 2 bottle jacks and a floor jack)
Edit: If your differential has never been out of the car you should do multiple applications of PB Blaster at all the bolting locations as well as the axle splines at the hub.
It will help in dis-assembly. (This was my third time swapping the diff in my car)
1)Loosen lug nuts and jack up rear of car at diff pumpkin.
2)Jack stands on frame rails just in front of diff cradle
3)Remove rear wheels
4)Disconnect exhaust if applicable (Do not need to remove)
5)Unbolt rear sway bar on both sides from top of link and rotate upwards out of the way
6)Unbolt axle shaft nuts at stub shafts on diff. This works well with an impact wrench otherwise you will have to possibly vise grip the rotor. I use a piece of rubber to protect from the jaws of the vise grip.
7)Remove rear brake caliper and tie up to springs.
8)Unbolt bottom shock mounts and move aside
9)You do not need to remove the axle shaft from hub. If removing axle shaft then use 32mm socket. Again, impact wrench is your friend or you might have to vise grip the rotor once again.
10)The axle shaft is spring loaded. Push cup toward hub to remove from stub shaft. The axle should slide out from hub at this point. If not then manual manipulation with hammer and 2x4 to release from hub spline. (Caution! This could separate your wheel bearing at this point depending on the severity of rust holding the axle in the spline)
11)You can see with this picture that the cup is removed from the stub shaft and the axle is just hanging.
12)Unbolt drive shaft at pinion flange. (Do not lose special shoulder bolts) Push Driveshaft forward and drop down or remove from transmission. (Trans fluid could leak out if you remove)
13)Unbolt Sublink bar from diff cradle
14)Center a floor jack under diff cradle just under pinion and jack up just enough to apply pressure and keep in place when removing subframe brackets on left and right side of subframe.
15)Position the other floor jack directly under the pumpkin of the differential and jack up to apply pressure but not lift.
16)Remove the bolts for differential mount to body and slide the bottom bushings off.
17)At this point lower both jacks simultaneously to keep the cradle and differential level until the cradle/differential mount guide bolts coming from the body are almost completely through but not all the way out of the guide holes.
18)Unbolt the 2 pinion mounting bolts holding the differential pinion to the cradle and remove the 2 hole washer.
19)Lower both jacks some more but again keep level and don?t let the front cradle guide bolts completely come out of the guide hole in the bushings
20)Now just lower the differential to slide off the guide bolts coming from the body. Let it angle down to slide the pinion mount up and off the cradle mount. Just keep lowering until you can slide the differential out from underneath the car.
Installation is the reversal of the steps.
A note of caution, once the differential is slid back in place and the 2 pinion mount bolts slid up and over the cradle mount be sure to raise the cradle and differential simultaneously and level. If you don?t the assembly will get hung up on the cradle/diff guide bolts and you will have to employ the use of crow bars to realign.
This whole process can be done by one person but 2 are so much easier.
Approximate time of completion from jacking the car up to dropping off the jack stands is 3 hours for one person.
I took my beer break after the car was dropped off the stands.
