I just clean them with whatever standard cleaner/solvent I use on my guns..."gun scrubber", "Ballistol", "Shooters Choice"... or whatever....
I dissassemble and clean my dies about every 3,000 rds thru the press.../ same as recommended by the press mfg for lubricating press...( so I do everything at once...or every time I change calibers on press --- clean press, lube, clean dies in toolhead, etc...).
Q tips, a couple of patches.. no big deal...