Go to the jeep dealer and pick up a tube of RTV Mopar part number 82300234, I prefer a gasket but RTV works fine. Jack up the jeep on stands, loosen all the bolts around the cover, remove all but the two top ones. With a catch bucket underneath pry the cover off, I use a narrow spackle knife. The two bolts on top prevent cover from falling off into your catch bucket and soaking you with lube. If you have a limited slip rear pickup a bottle of the friction modifer, it's about 3 oz or so. Pickup about 2-3 quarts of gear lube, that should do it. Depends on whether it's a D35 or 8.25 chrysler rear. Clean the cover and remove all the old sealant from both the cover and the diff housing. Put one continous bead around the cover making a U at each bolt hole with the bottom of the U on the inside NOT the outside, make the bead between a 1/4 and 1/3 inch wide. Have plenty of rags and some electrosolve cleaner, the kind that dries with no residue and clean the housing out, don't be afraid to use the whole can of cleaner, it won't hurt anything, use the rags to clean it out. Put the cover back on, tighten and pour in the first bottle of lube, add second bottle and as soon as it starts running out the hole it's full. Lower and take it for a drive then bring it back, up on the stands, pop the cover and see where the level is, add more lube as needed. If you need to add the friction modifier add it after the first quart of lube. Thats about it, front works the same cept the filler cap is threaded unlike the 8.25 where it's a rubber plug.
It should be on level ground when you check the diff fluid.