I end up cleaning my Componons nearly every year; they seem prone to some sort of haze. Fungus is also a problem aggravated in my darkroom. I tend to keep most of my enlarging lenses (I have way too many) in our one air conditioned room in the summer months.
Anyway, the are easy. You'll usually need a spanner, but not always. A gripper is nice and sometimes enough if you only need to get to the surfaces either side of the diaphragm; I use pieces of bicycle inner tube for grippers. I use mostly microfiber clothes, but also some cleaning tissue. Your breath is likely the only cleaner you need. I do you ROR sometimes (see B&H, Adorma etc if it still exists), but once you start with it, you clean and clean to get get all the oily residue off that it releases.
The lenses varied over the years. Post a picture and one of us might have some thoughts on your particular lens. I've mostly switched to Nikkors, so my Componons tend to be older. I'd say with those, the biggest tip would be to have it sitting flat on a surface, face up, when you take the front group out; you may have a tiny ball exposed that makes the clicks for the aperture. The back can often just be unscrewed with a gripper or spanner. You can carefully get to the rear surface of the front group through the diaphragm, but I prefer to pull the front for easier access. I liked canned air for blowing dust off surfaces just prior to assembly, but be careful with it around the diaphragm.