I use a Finish Line chain cleaner because it uses the least amount of cleaning fluid, 1/2 oz. The tool breaks maybe once every five years or so otherwise, I'm satisfied with it.
For cleaning fluid, I buy a citrus degreaser in one gallon containers found at the big box hardware stores. When I can't find that, I buy Simple Green is the same size. I'm about to run out of the citrus and go back to the Simple Green I purchased, but if I recall, the citrus does a much better job, so you might want to stick with citrus-it's much cheaper by the gallon than bicycle specific degreasers.
I pour the fluid in, clamp it over the chain, and turn the cranks for about a minute. I never have to repeat the application. I then fill the chain cleaner with water and repeat. This is not something you do in your garage or basement; I perform this work in the parking lot.
I believe Lennard Zinn from VeloNews reported about chain cleaning recently and mentioned that with today's special chains, connecting pins, and tighter tolerances, removing the chain for cleaning is not advised. So find an on the bike method that works for you.