My current process:
I start by taking it all apart. My turning tray is removed prior to hatch so its rarely dirty. Lid, base tray, and bottom (water tray). Its too big to put in my sink and I don't have a bathtub so outside I go!
I grab my "kit" which is a pile of stuff specifically for cleaning my incubators. 3 rags, dish soap, old toothbrush, and a bucket.
First step, I take the toothbrush and start dry scrubbing the base tray and water tray. Most of the debris flake off. Then, I mix up some warm soapy water and pour it into the water tray with the base tray sitting in it and then leave it to soak.
While that soaks I move back to the lid, using one of the dry rags I wipe out all the fuzz. This last time I used an air compressor with an attached wand to gently blow out the fuzz that was stuck in the fan and electrical. I am never going back! Easiest it has ever been to clear out the fuzz! Magical!
Once the lid is done I move back to the soaking trays. I take rag #2 and roughly wip everything down, still in the water, to get all the heavy bits. Then I go back with the toothbrush to get the crevices and stuck on bits.
I drain the soapy water then rinse, rinse again, then I use my last rag to wipe off the excess water. Lastly set out to air dry for as long as I can.
My incubator is fairly big, bulky, and overall awkward to handle. For my next hatch I'm gonna start incorporating disinfecting too just to play it safe (I typically use fairly warm water to kill germs). I'm planning to do roughly 10 hatches this year so hopefully I find more slick ways to clean things!