C-clip axles generally require that you remove the crosspin in the differential carrier, so you can press them inwards, and then remove the C-clip. Then, you pull the axle shaft out. Reassembly is the reverse of removal.
With non-C axles, you don't even have to take off the cover (but it will help.) Remove the bearing retainer plate (behind the brake drum - the same screws retain the bearing plate and the brake backing plate) and pull the shaft out. You may need a slide hammer - or use an old wheel or brake drum to get a good whack in. You then remove the bearing race (which should work with finger pressure only) and put in the new shaft, seal, and bearing.
The catch? You'll have to have the new shaft with a new bearing already on it - it takes something like a 5-ton press to change bearings. You can cut them off with a Dremel (get far enough through the race and it will crack from internal strain,) but you can't put them back on in the field.
When you carry spare shafts, make sure the bearings are NEW, well-greased, and then wrap them in plastic of some sort to keep the grease IN and the crap OUT. Several layers of cling wrap should work well - so does waxed paper retained with rubber bands.
The reason for removing the cover when changing non-C axle shafts is so you can guide them into the side gear (if you need to,) or so you can push the side gear back into place (if you move the thing.) It shouldn't move - and you can usually guide the axle into place with a finger down the centre hole, or just use some "guiding pressure" on the hub flange to get the shaft in. Once you get some practise at doing the job, all you'll need to do is jack that side up - to remove the tyre, and so you don't lose too much axle lube...
5-90
