good stuff above, a couple of different ideas...
first read this http://www.pavementsucks.com/tech/diff.php
the old differential fluid does stink, but i did mine in the garage anyway (where its level) and just drained fluid into a pan.
i did both front and rear at the same time. jacked up both ends and set on jack stands so i could rotate wheels and inspect everything.
i just used regular fluid, 75w90 or 80w90. its cheaper than synthetic.
i think it took about 1 - 1 1/2 qt per axle, can't remember exactly.
loosen the front drain plug while the cover is still attached, just in case its super tight.
when prying the covers off, do NOT bend them or scar them.
scrape out any sludge in the bottom of the case with your finger, then spray out the case with brake cleaner.
wipe out excess and let it evaporate. DONT lose the magnet in the bottom, its supposed to be there.
clean cover and case, a scotch bright pad works good to get off old rtv or gasket sealer.
i used the black rtv so it wouldn't be red or blue and look silly. not sure if black is hi temp or not but doesn't need to be.
if you have a limited slip differential you will need the special oil additive. look on rear axle driver side for label,
open vs locked (limited slip).
try not to get it on your clothes, it really stinks, did i mention that.
do NOT drive wifes car with any oil on your clothes, skin, hair, or nice oily rag. you'll never hear the end of it.
if you see any milky white stuff, its water.
not sure why, but after changing mine, one front side leaked a tiny little bit for a couple of weeks, then quit. might have been a tad over full.