It's pretty easy, but there is something important you need to be aware of first - when all is said and done it's possible the contact pattern of the gears is no longer ideal (assuming it was ideal t begin with), personally I've never had that happen with a Sterling rear axles and I've had 3 carriers and 2 sets of gears in the same axle housing and it always came out near perfect, but still it's possible.
If you still wanna proceed, his is how I do it: first order of business after pulling diff cover and draining oil is to clean the gears, "paint" them, and check contact pattern, take plenty of pics of said contact pattern to have something to compare to when the new carrier is in. Then undo the eight 7/16" bolts (they take 5/8" socket) in the center of each rear hub and pull axle shafts out a few inches, wheels can remain bolted on and for that matter there is no need to even lift axle off the ground (that's the beauty of full-float axles). Back at the diff mark the carrier bearing caps as left and right and which way is up and down (they should not be mixed or flipped over) and undo the two big bolts on each and pull the caps, then carefully yank/pry the diff out the axle housing. On each side of the diff between the carrier bearing outer race and the axle housing there will be a thick shim, just like the bearing caps these cannot be mixed or flipped so pay attention which one goes where and how it sits. Once diff is out of the axle stand it on its end on a large piece of wood, then heat the ring gear evenly with a propane torch, then grab an impact wrench and remove the 12 bolts holding the ring gear, the gear may at this point simply fall off the carrier - if it's stuck you can add some more heat to it (no more than 200F tho, so don't go medieval with an oxy-acetylene blowtorch), then smack it with a dead-blow hammer and it will drop off. Do this with both axles, clean the oil out of the bolt holes in all carriers and gears, switch carriers, then reinstall the ring gears (heating the gears may be necessary again) - I like using Dana 70 ring gear bolt upon reassembly cause they are stronger and also have serrated heads with tiny teeth that grip into the carrier and prevent the bolts from backing out on their own, additionally I apply red Loctite to the threads of said bolts for extra insurance. Then it's time to reinstall the diffs back in the axles, I usually just put the driver-side preload shim in place, drop carrier in and slide it to the left as far as it will go, then carefully tap the passenger-side preload shim in place with a dead blow hammer (it can fracture if hit too hard with a steel hammer), and finally reinstall the bearing caps with loctite on their bolts. Note that it is very important that the ring gears and carrier bearing caps and carrier preload shims all stay with their respective axles, while the carrier bearing races stay with their respective carrier and thus migrate between axles - the idea is to keep the wear items (bearings, gears) as matched sets, and the gear pattern setup components (preload shims and bearing caps) are axle-specific to begin with. Finally check the gear contact pattern as best as you can and compare it to the pics of the initial setup, if it all comes out good then you slide axle shafts in and close axles and fill with oil.
Lemme know if you think you can handle this work so I can dig out the part # for the D70 bolts and also the torque specs for the different bolts so you don't snap something and end up with a mess on your hands.
