Open your Factory Service Manual (FSM) and open it wide. If you don't own a dial indicator don't bother opening the book. You also need a torque wrench you can use counter clockwise and a special tool for adjusting the carrier bearings.
Essentially what you have to do is pull the cover, pull the cross pin, push the axles in one at a time to remove the C-clips, remove the axles, check the ring gear backlash at a few places on the ring gear with the dial indicator, loosen the carrier caps, back off the bearing adjusters with the special tool, remove the bearing caps and differential. Then remove the ring gear bolts, tap the gear off the carrier, put the ring gear on the new carrier with new bolts, put the carrier back, replace the caps, adjust the carrier bearings/ set the gear backlash and bearing preload, put the axles back, put in the C-clips, put in the cross pin and it's lock-pin, replace the cover with a new gasket or RTV and refill with GL-5 and the limited slip additive. Should take about an hour, maybe more.
