Citrus degrease followed by isopropyl alcohol for new / race chains.
Training chains I just put them straight in, the liquid wax is quite effective at removing dirt, with a little agitation. I use a bent spoke to stir / move the chain and remove it from the wax.
Put it in a robust plastic bottle such as an old bleach bottle, quarter fill with white spirit, shake like f**k, pour out the gunk into an other bottle. The gunk will settle out after a time and you can reuse the white spirit. Wipe and allow to dry.
What's the best way to clean a chain before dunking it in wax? And how often do you have to reapply?