Everyone should have one of those spiny chain cleaning plastic things but I have not used mine in ages yet still do not intend to give it up...
I found my best chain cleaner by accident. I normally lube then wipe my chain down with a rag almost every ride but then again I ride dirty dusty asphalt and pretty much my whole bike is kinda dirty.
Once upon a time, before a short ride with friends I pulled my bike out and hit the chain with a garden hose pressure nozzle just spinning it around and really spraying directly in-between the links. No solvent, no scrubbing, just plain water. (yep it was a little messy but I was pressed for time).
When I went to put on my regular chain lube I was amazed at how clean the chain was. There was no grind sound or feeling when twisting the chain sideways and after a wipe down was more than expected ... Clean.
So thats the way I do it now...
Rem: I don't have a million dollar bike and I don't use high dollar chains. If I did then this might not work.