Just finished this process...
The way I did this was the only way I've done it in the past on other vehicles. I wish there was a bottom plug to make the drain process easier,but unlike some vehicles, there is not. Mine is an '03 so it may be different on other models. I have the yukon SLT, NOT THE DENALI, so the process may be different for that model.
It was pretty simple, I placed an oil catch under the diff, cracked the cover bolts, let it drain completely.
Once drained, I cleaned up the area of all the oil and tightened down all the bolts. Now, just from habit, I followed a criss cross pattern and tightened them down in a stepped pattern.
Once tightened back up, I used a 3/8" ratchet, located and removed the plug. It sits on the front passenger side of the diff, look towards the driveshaft from the rear. It's pretty hard to miss.
Now, I know it's not "the best" in some peoples opinion, but it was readily available, so I went with Mobil 1 synthetic 75/90. I initially bought only 2 quarts, after reading a post on here regarding the required amount.
I put in the 2 quarts, replaced the plug and took it for a test drive. It had a "smell" to it when I got home, so I did more research and found that others had used closer to 3.5 qts.
I added a full 2 more qts, total was 4 quarts to fill it up. I found that it was easiest to use some old clear fishing tank tubing...it was clean and unused! I cut the tubing and placed over the cut nipple on the bottle. Worked great for me, filled her all the way up I believe.
A side note, make sure you are on a flat surface! I started on a slight incline with the nose down...thought she was full, then turned it around and finished filling.
Aany questions or help, let me know.