I think it's like flossing our teeth, meaning doig it is more important than how you do it. looking at mine today, I remembered it didn't have a cleaning in a long time & needed it's "annual" cleaning. still could have done a more thorogh job. a simple chain cleaning tool wasn't going to remove what it needed removed. also depends on what riding you do. street riding or off road. my MTB chain had a mixture of God-only-knows-what. plus it seems, whenever I clean something, I wind up cleaning the things next to it, such as rear cogset, front chain rings & both derailleurs
straw brush dipped in mineral spirits was productive but didn't fit in every other narrow link
found some pipe cleaners. doubling them over was the best thickness for the narrow links
basically it was combined particles of everything on the planet that I've been riding over, this past year, with an interesting mix of binders forming resilient fibers. mud, soil, pine needles, leaves, sand, twigs, minuscule road kill?, stone dust, all manner of detritus, grime & chain lube
an empty whisky nip, full of mineral spirits, was a good small container for dipping the brush & pipe cleaners into
cleaning ea link let me find the master link, so I got the Park tool & removed it
I was tempted to soak it in 3 pickle jars but opted not to this time. instead I cleaned it more by hand then set it to dry, while I cleaned the rest of the drivetrain. after a cpl hours I lubed it by hand & flexed ea link. when I found a link that wasn't flexing as smoothly as the others I lubed it more & flexed it until it felt better. then wiped it continuously until the dry chain lube actually dried. & put it back on. not sparkling, but a heck of a lot cleaner & more functional. did a test ride in the parking lot. btw - taking the chain off the bike let's one clean, actuate & lube the derailleurs much more easily w/o the chain getting in the way!
btw the rear gears are best done with the specific brushes for getting into that area for mechanical cleaning (but after looking at this photo, I went back out with a steak knife, to get the remaining circle of grit)
shame on me for abusing & neglecting this bike's drivetrain, for so long