I mean, its hard to fully explain since there's no hard rules, mostly just getting a feel for it - but I can try? I suck at explaining I fear I truly do not think when drawing I just Observe and Apply with no thoughts at all
but uh. have an attempt
General good thing to note: Don't go overboard with it. I often end up forcing myself to erase some of my AA at the end of a sprite because otherwise I ahve too much going on and things start looking blurry/not gen 5 style inspired anymore real fast. For AA usecases though, mm.
-An inbetween color for AAon a single shade , like the purple on my Cress/Gard. Its mostly there to soften edges of the shadow, since the main and shadow color are quite far off eachother. I also like dithering for clothing textures, so it could be used for that as well. Generally speaking I try to stick to an inbetween color on a single shade for max 1 per sprite, in this case my the purple. Whats the difference between a full new shade of the color and an inbetween shade of it? Uhh. mostly just how often it's used haha. In this case- almost entirely exclusively for AA on the shade. Worth to note this is the one that's least common for me, usually it's not necesarry. But if you feel one specific color and shade are just too harsh next to eachother it can work real well to soften it up a bit
-AA between patterns/colors right next to eachother, not seperated by lines. Example here is the Ho-oh/Milotic. Fairly straightforward: A transition color, somewhere inbetween the two colors you're connecting- so that it doesn't look too harsh.
-AA Along the edges, mainly to round out shadows or harsh angles in lines. Using my Gardevoir/Goodra here- there's AA used a lot along the edges to sell things looking round, like the legs, and the tail. Obviously in pixel art you cant draw an actual round line, but AA can really help sell the feeling of one!
-AA for faces. This is generally the area where I have the most AA going on- expressions are hard to do when you have all of 9 pixels to work with, and AA can help make some expressions read better from afar. I have no rules on how I apply it in faces, but it's worth noting I generally use more AA on a small space then I nromally ever would when it comes to faces, just to help them read better from a distance. Last three pics as example here- usually I have most of my AA around the eyes specifically in a futile attempt to get more subtle expression notes to read