Sad cigar 


First, make sure that the ashtray is solid brass. Check with a magnet - solid brass is not magnetic.
Next get the secret cleaning sauce - Ketchup

Apply liberally

Get an old tooth brush and some elbow grease

Voila! Happy cigar 


The acidic property of the ketchup is just right for removing tarnish from brass and copper.
  ...now to get it dirty again. ;^)