I have an air compressor. If I was using canned air I think it would take too many cans!
I use compressed air to blow the black dust off the coils.
I have a small 1 inch paint brush. I pull the lamp boards off the bottom of the playfield.
I spray the paint brush with a detergent (sometimes purple power, sometimes a product called simple green (diluted)). Any soapy detergent cleaner will do. I get the brush wet, but not dripping.
I push the bristles of the brush into the insert on the bottom of the playfield and quickly brush the underside of the insert.
Then I immediately use the air compressor to spray dry the insert. If it still has lots of dust, I do the same thing again, cleaning my brush (spray it down with detergent water, pat it dry to get it mostly clean), between each use.
The air compressor makes sure that the moisture doesn't cause the wood to swell... liquid is only on the wood for a second or two.
It takes longer to describe than to do.
Cleaning the bottom of the inserts makes a BIG difference, and just blowing the black dust out isn't enough to clean them.
As for the wood, a soapy damp rag, and where there is a lot of grime I'll do some sanding on the bottom of the playfield for appearance. Keep liquid off the wood by immediately using the air compressor to spray dry as you wipe.
This is NOT the procedure to use if you are restoring a pin! Particularly if you are restoring it for someone else!
This is what I do when I 'shop' a machine for resale. I'm doing this level of work for 'players grade' machines that I tell customers are 'clean, but not restoration level clean'.
I'm very meticulous on the top of the playfield to get every speck of dirt and grime I can. Under the playfield, I want the mechanisms to work, the lights to shine cleanly through the inserts, and I don't want anything embarassingly dirty, but for the 'players grade' machines I'm working on, I don't clean the bottom as well as I do the top.
Finally, I use a damp soapy rag to wipe down the wiring bundles. A restoration guy would pull all the wiring (!) and ultrasonic clean the harnesses. I just wipe everything down.
But the lamp boards.
All the lamp boards with connectors get pulled and put in the sink. I remove all the sockets and the bulbs. I wash with soap and water and then quickly dry the boards with the air compressor. All the bulbs will be replaced, and then every pin on every lamp board will be touched up with fresh solder.
Any relay boards, motor boards, etc, will be pulled and likely have the solder reflowed. Trough opto boards will frequently get fresh opto transmitters and receivers.
I lightly 'tug' on all of the wires to the coils, looking for anything poorly soldered or wires that are almost about to break off due to vibration. I generally won't resolder every coil.
This is after I have completely rebuilt the flippers, and inspected/repaired all the mechanical assemblies.
That's pretty much what I do on the bottom of the playfield.