When I got my used Cimbali Jr grinder, I tore it down completely removing all the outer sheet metal and cleaned it up and put it back together. I did not go so far as to remove the doser completely, but I did remove the doser top and vanes. Removing the body sheet metal was a bit disconcerting as it took a great deal of force to back the lower screws out of the cast frame. I thought I was going to round off some screws. The doser top also wasn't too much fun so I would avoid that as well.
Now for regular maintenance, the above isn't necessary. I just wanted it like new before I used it.
So this is what I would do:
Remove hopper, via 2-4 screws inside the hopper.
Wash and dry hopper.
Once you have the hopper off, if I recall you will see the top black trim ring and the worm drive mechanism. I know I removed the trim ring, but you may not need to, I can't recall.
Remove a few screws that hold the grind adjustment ring to the top burr carrier, remove the grind adjustment ring. If I recall this has two parts, an inner and outer ring, make note of their orientation.
Thread out the top burr carrier (big brass body), you will clean this up in a minute.
Now you will see the bottom burrs that are attached to the motor shaft. You probably see lots of coffee grinds/beans and build up.
I removed the bottom burrs to clean them and to clean under them in the grind chamber. I used one screw driver to stabilize the bottom burr holder to stop it from spinning, and another to back out the screws holding the bottom burr.
Clean things up with a whatever you feel appropriate, grinder brush, nylon or brass bristle brush, vacuum, moist paper towels, you get the idea. I did not remove the top burr from the top burr carrier, I felt I could get them plenty clean as they were. I washed the bottom burr set so that it would install without any grinds under it.
While you have it this far apart, I would brush and vacuum out the grind chamber chute.
Put it back together, the only step you need to take caution with here is to find the zero point and reinstall the grind adjustment ring such that the numbers are oriented properly at zero.... you can only get so close to zero, mine is about dead on. If you seem like you are way off from where you were check your reassembly.
Here are some internal pics so you can see what you are about to get into: