Remove the diff cover. Then remove the pinion shaft bolt, pull the pinion shaft out. Remove the tire and drum for the side thats leaking. Push the axle in and the c-clip should come out. Then pull the axle out. Look inside the axle tube and you can see the axle seal. Large screw driver or pry bar will pop the seal out. Don't scratch the hosing.
Sounds to me you have a Chevy product. Once the wheels are removed, dissasemble the brake shoes from the backing plate and emergency cable. Make sure the car has jack stands under it. Remove the rear axle cover. There should be 2 clis that will need to be removed. One on each axle inside of the pig. Then remove the 4 nuts that is holding the axle to the backing plate. Start to pull the shaft on slowlly. The seals are pressed into the axle housing. Be careful when putting back in not to damage the seals. Do not forget to install the clips back to the axle shafts when they are in place.