There are several older threads that discuss dial cleaning.
The likelihood of success is really dependent on the type of dial and you really need to consider the Hippocratic oath - "First do no harm".
The least damaging level of cleaning is Rodico putty that you can get from lots of watch / jewelry supply places. It's great for removing dust, dirt, grime, finger prints and stuff like that from all dials.
For lumed dials you're pretty limited to Rodico since anything wet will remove the lume.
For enamel dials you need to be very gentle and not rub or the enamel will be lost or faded.
Butler finished and white painted dials with gold numerals or markers are the best candidates for cleaning in my opinion and it's best to remember that "slow and steady gets the job done".
I've had some remarkable results using a jewelry concentrate like
Hagerty's Jewelry Concentrate.
All I do is put a few drops on the dial and let it soak for a minute or so, then rinse in warm (not hot) water. Then I do it again, and again, and again, until tarnish and grime is gone. It may look like crap after the first pass but it will look better as it goes from totally dirty to partly dirty to partly clean to mostly clean. Stop at mostly clean - I'm not a miracle worker here.
I have an ultrasonic cleaner and I'll rinse it in there but only briefly as the ultrasonics can lift the printing off the dial.
That's my secret, don't tell anyone. :wink:
Here's a recent before and after:
and after...