I often use BikeWash to clean my bike and my chain. I also have used the chain cleaners referenced here. They work well too.

If you can get your bike off the ground so that you can move the wheels, cleaning and lubricating the chain is much easier. You can find portable stands on the market- lots of bike shops sell them. Then the challenge is to find a place where you can do the work!

Cleaning up afterwards? Believe it or not, I use Tide powdered detergent. I put some under my nails and scrub away with a nail brush. Result- clean nails, no grease or black stuff anywhere.