I also highly recommend buying the crush sleeve eliminator from Summit (Ratech 4105
Here's how I would do/have done the bearing replacement with the crush sleeve eliminator:
1) Remove diff cover
2) Measure current backlash with a dial indicator and write it down somewhere.
3) Check current pattern with marking compound and take a pic
4) Remove carrier
5) Remove pinion, yoke, seal, and bearing races
6) Remove and replace inner pinion bearing. Be sure to reinstall the shim that's under the bearing. You might have a shop do this part as it requires a bearing puller and a press if you don't have them.
7) Install new races in housing
8) Install pinion, crush sleeve eliminator with a few shims, outer bearing, oil slinger, yoke/flange, washer, and OLD pinion nut. Leave the new pinion seal out for now. Edit: If you measure the old crush sleeve, it will give you a good starting point for selecting shims.
9) Slowly torque the pinion nut to 125 ft lbs, checking the pinion bearing preload as you go. Add or remove shims from the spacer kit until you reach about 15-25 in lbs
10) Install carrier
11) Recheck pattern and backlash
12) Remove carrier and pinion and reinstall with new pinion seal and new pinion nut with red loctite
13) Torque pinion nut to 125 ft lbs
14) Replace diff cover and fill with gear oil!
Straight off Google from a jeep site, yeah Jeep but it was on an 8.8 Ford.
Depending on your mechanical ability I would have a shop do it, there are a lot of precise measuring and torquing going on here and if you mess something up say hello to a grenaded diff.