Removing the c-clip, which holds the axle shaft into the axle housing, is a simple process you can do yourself with some basic hand tools. The c-clip itself is a small part inside the differential that holds the axle in place. When the c-clip is removed the axle can be removed from the housing.
If the differential is still on the vehicle, you will need to loosen the lug nuts of the wheels on that axle. Chalk the wheels opposite of the axle you are working on and jack the vehicle up. After securing the axle on jack stands, and moving the jack out of the way, remove the wheels from the axle you are working on. Place the transmission in neutral. With a drain pan in place remove the bolts holding the differential cover in place. If the cover sticks in place you can gently pry if off or try tapping it with a rubber mallet. Once the cover is removed let the gear oil drain from the axle housing. Using brake cleaner or engine degreaser, clean the inside of the axle housing. If need be, use a rag to scoop the remaining oil and cleaner out of the axle housing. There will be a magnet either on the differential cover or inside the axle housing, be sure to get as much of the metal shavings off of this magnet as possible so you do not contaminate the new gear oil. After everything is clean it will be much easier to locate and remove the c-clip from the axle.
If the axle you are working on has drum brakes, you will need to remove the brake drum to access the axle. Grab the brake drum with both hands and twist and pull. The drum may be stuck and one or more of the following methods may need to be used to remove it. The first thing to try is adjusting the brakes down. On the backing plate, there should be an oval rubber seal that when removed gives access to the brake adjuster. Back the brakes down using the adjuster and try removing the drum again. If it is still stuck the next method to try is smack the edges of the drum with a hammer. The last thing to try is using a pry bar between the drum and the backing plate.
Once the drums have been removed and you can see the axle, push the axle in towards the vehicle until it bottoms out. Now you are ready to remove the c-clip from the axle. The c-clip is located in the axle housing and is on the end of the axle that is visible between the gears. Spin the axle around until you can see the c-clip and using a screwdriver, a pick, or a small magnet removes the c-clip from the axle.