i don't know what kind of axle you have, but I can contribute from the standpoint of a 10-bolt. For a 10-bolt, you will remove your carrier by removing the caps on each side of the carrier. When you remove them, note which side they came off and which way they were pointed. You must put them back on EXACTLY as they came off.
Then, remove the carrier keeping track of what shims are on each side. You will need to put the same shims back on the original sides in order to keep your gear mesh the same. DO NOT LOSE OR MIX THE SHIMS or you are screwed. The carrier is heavy. Weighs about 20-30 lbs. The teeth on the gear are sharp. You may need a crowbar to get the carrier out. Or, rotate the pinion via the driveshaft. This should "walk" the carrier out.
When removing the ring gear, you will need to secure the carrier in a vise of some sort. In addition, the ring bolts ARE REVERSE THREAD. When you remove them, you should throw them away. You should never reuse ring gear bolts. Now you can do what you need with the carrier.
When reassembling, use new ring gear bolts with loctite and torque to the proper setting. Reinsert the carrier into the housing. If it is snug, put in whatever shims you can and "drive" the others in using a rubber mallet. My shims from the factory were single thick shims. If I had the carrier out slightly, I could get teh shim started. I then used a pry bar and a rubber mallet to drive the shim and carrier into the housing together. Once all shims are in, rebolt the carrier beraing caps exactly as they were removed. Torque them properly and all is done.
Here are the torque specs for the various axles/carriers. I know for the 14 bolt, it uses dial adjusters instead of shims for the carrier. If you are dealing with one of those, note the exact position of the dial adjuster before removal. Note exactly how many turns you "undo" the adjuster for removal. Reapply the exact number of turns after installation.
I hope this helps some.