Well, the best would be to read the USMC manual. That's a very generic, proved to work procedure for cleaning.
1] Don't clean the gas tube, it is unnecessary. Build up gets blasted out. It is "self cleaning"
2] AR's like to be wet. So lube them up well. Don't drench them, but do not oil them like your daddy's bolt action or lever gun. Carrier and bolt should have the wet look to them.
3] Main areas to focus on are the bolt, and that included cleaning under the extractor, and cleaning the carrier. Also, the barrel (duh!) and special attention to the chamber and the locking lugs. I like to use a shotgun brush or something large which cleans that area out fast.
So, that's the main areas. The entire bolt carrier group, and the chamber. Take care of those and reliability will be good. Obviously, you should clean in other areas too, like the inside of the receiver and the buffer and the lower and everywhere you can. But the critical areas I listed above.
Finally, brake cleaner is your friend. I don't waste time anymore. I put out the parts and blast them with high pressure brake cleaner. All the sludge just cleans off in no time. Then I blast them with CLP from a spray can. Excess is blasted off with compressed air (that also forces the oil into every tiny crevice) ...
I use a lot more fluids, but my cleaning takes 5 minutes flat (not counting bore cleaning) and I get it cleaner than people who sit there for an HOUR or more with brushes, cotton patches and dental picks.