so the 'right' way to clean is with an ultrasonic cleaner, but that isn't really necessary.
here are the very basic tools and supplies you'll want... note that the 'real' guys would use the 'right' tools and deal with subtleties you won't even be aware of until down the road a bit. in the meantime, this will cover what i consider absolute basics.
tools and supplies:
-- needle nose pliers... one regular set, one brass-lined
-- small and medium flat blade screwdrivers
-- 90% alcohol
-- toothpicks
-- some clean old t-shirts for drying parts after you wash them
-- some kind of degreaser (i use super clean... don't breathe it!!!)
-- dawn dish detergent and sos pads
-- toothbrush
-- paper towels
-- compressed air (like used to clean camera lenses)
-- 2000 and 4000 grit wet/dry sandpaper (amazon)
-- some kind of magnification... i like these but also have clip-on monocles for my glasses:
https://www.amazon.com/gp/product/B07T4KPYN2/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1
-- one of these:
8" Double Ended Spring Hook (Pack of: 2) - S1-20241-Z02 | eBay
1. take it apart (don't worry... this part is the easy part!!!)... start by removing the pieces in front of the front plate. remove the pins and place them on a piece of paper where they won't get disturbed, in roughly the places you found them... for example, upper left pin holding rack arm would go upper left of your piece of paper. in addition, TAKE PHOTOS AS YOU GO... LOTS OF PHOTOS SO YOU'LL BE ABLE TO FIGURE OUT HOW THINGS GO BACK TOGETHER!!!
2. note that you will have strike pieces (the arms that trigger the hourly strike) and motion works pieces (the brass gears in the middle that move the hands. lay them on the piece of paper, as well
3.start degreasing and then washing all pieces. be very careful... you do NOT want to snap one of those small pivots off or drop a gear and bend (or break) a tooth. GO SLOWLY. repairing any of these parts is above your pay grade and you would have to send t to someone to repair. use the toothbrush dipped in soapy (the dawn) water and gently clean each piece. as soon as you're done with each one, dry it off... first by t-shirt, and then by blow dryer, and then by wiping it down with paper towel and alcohol... and then blow off any remaining dust or lint with the compressed air. you can try the sos pads on the plates if there are areas that won't clean up... but always be gently and go slowly. clean is the goal... bright, shiny and even is not.
4. clean out every pivot hole you can find (don't really need to do screw holes) using clean toothpick ends and alcohol... twist and remove, check for schmootz, repeat until clean. note that the 'real' guys will tell you that toothpicks aren't hard enough to do the right job... but we're working under the 90:10 rule.
5. gently gently gently clean the pallets of the verge with toothbrush and then polish using the 4000 sandpaper.
6. see if you can reassemble the cleaned between-the-plates pieces... but NOT the verge/crutch assembly or strike hammer. some people reassemble to the front plate (lying upside down), but i prefer to load the back plate and then (CAREFULLY) add the front plate. the procedure is to put the pieces in the back plate and then GENTLY lay the front plate on top. line up the winding arbors, minute hand arbor and second hand arbor (BE CAREFUL WITH THIS ONE!!!) so they go through their front plate holes... and then gently (without pressing hard) slide the remaining pivots into their respective holes. this is where you DO NOT want to apply any sideways pressure to the pivots as they can break. this is where you DO NOT want to apply any sideways pressure to the pivots as they can break. this is where you DO NOT want to apply any sideways pressure to the pivots as they can break. this is where you would use the double-ended spring hook CAREFULLY to help get the pivots into their holes.
7. once you have the front plate added back, turn the great wheels by hand and watch things spin... you will have earned the good feeling.
take photos of where you are and the remaining pieces and return here for more assistance.