I just did this last week.
Just like it's been said already... Remove all the cover bolts except the top 2 or 3. Just loosen those. Pry the bottom of the cover away from the housing with a screwdriver. The old oil is going to pour out everywhere, so have a large, deep pan (like a cat's litter box) to catch it in.
If you have the car jacked up at the rear only, you'll still have some old oil left in the housing. You'll need to scrape it out of the housing by hand. Don't do it with a bare hand. There may be small, sharp bits of metal in the bottom, so use a scraper of some kind, or use a lint free cloth.
Closely inspect the gears, and look for excessive wear and/or chipped teeth.
If you need new axle bearings or seals, now is the time to do those since it'll just take a few minutes to remove the axles. They're cheap and easy to do, but require some special tools that can be borrowed from AutoZone.
Clean the old sealant or gasket material off the housing and cover with some brake parts cleaner and a putty knife.
Using RTV sealant is recommended instead of a gasket. Run a bead of it around the surface on the housing, making sure you run it to the inside of the cover bolt holes. Put the cover in place and put in the bolts, tightening them in a "star pattern", like you would lug nuts. Do not tighten them too much or you may distort the cover, causing a leak. Let the RTV dry for at least 6 hours.
Find the filler plug on the driver's side of the housing and remove it. You'll need a 3/8" ratchet, and probably a 3" extension to reach it. It does not require any socket.
Just under 2 quarts of 80W-95 gear lube (or 75W-140 synthetic), and a 4 oz. bottle of friction modifier will be needed to fill it (stock size cover).
Use a pump as suggested to put the 1st quart in, then put in the modifier. The Motocraft friction modifier comes with a small spout to help you put it in the filler port. Be careful not to spill the modifier or get it on you -- IT STINKS LIKE YOU WOULDN"T BELIEVE!!!!!
Start adding the second quart with the pump until you can feel the fluid level at the bottom of the filler port (or it starts to pour out onto the floor). Replace the plug. My stock rear end took exactly 2 quarts. Since I added the bottle of friction modifier, I was left with 4 ozs. of gear oil left in the 2nd bottle of lube.
Lower the car, and drive it like you stole it.