What you will do is jack the car up, and support the rear end on jack stands (Would hate to hear of an accident in the news.) Then you will take the read wheels off, the drums/rotors depending on trim level, next you move back under the car, and drop the drive shaft. It can be held on a number of ways, I think GM uses four bolts to hold it in place. Only drop the side to the rear end. Next get something to catch the old smelly, slimy, metal filled gear oil in, and remove the backing plate. It should be like ten to twelve 1/2 or 13mm bolts.
Now this is this is huge. Lay a clean rag down, and place any removed parts on it. Take note on how they come out, because the spider gears can be a nightmare. Slowly turn the rear end from where the drive shaft was till you see a small bolt head that goes into a rod. It should be something small like an 8mm. Remove said bolt, and rod to reveal two clips. These are clips for your axles, and should simply pull off. Next remove both axles, and you should not have to replace the grease seals. You can if you want since you are right there.
I believe the spider gear will at this point simply turn out as you turn the rear end. keep a close eye on how they come out so you can put them back in the same way. Replace them if they are damaged. Next you should be able to remove the main bearing, and begin reassembly. I would replace the front main seal just to be safe. Assemble in reverse, and you are done. Clean up the inspection plate, and remove any old gasket. Fill it up with the correct gear oil, and hit the road for a test drive to make sure everything is seated right.
Now that is how you do one in the ideal case. You will more then likely need a repair manual to know how to get the gears back in place. Even if you didn't need it now you can fix most anything on your car. If you have a manual transmission then the repair guide will be able to walk you through a complete tear down of your car, and rebuild.
I hope this is helpful to you. I just hope I didn't leave anything out as it has been a minute since I last worked on a rear end >.<