This is what the guys from Redding told me to do. Use what you normally use to clean your guns.(Hoppe's,Shooter's Choice,Butch's,whatever) I use a nylon brush that is called a tube brush. It is about 9'' long, with a wire loop around one end. I wrap a cleaning patch around it with solvent. Push it back and forth and turn it a few times. Wipe it out with a clean patch, and if I feel like it, spray some Gun Scrubber,Gunk Out, or even brake parts cleaner. This will take any oil off the dies, so make sure you wipe them down with some kind of rust preventative.(G96,Rem Oil,Break Free,something)
If you find a set of dies, that are looking pretty rough, completley disassemble them, and put them in your tumbler. That usually gets most of the crud off of them. gypsyman