In my view, the best way to clean your chain is to remove it and soak in the homebrew mixture I described above -- that is, 3 parts odorless mineral spirits to one part motor oil. Let the chain soak at least a few hours, even better overnight. Then dry it off well with an old rag and reinstall on your bike. To make matters simpler, put a superlink on your chain, such as the Connex/Wipperman link. Using a superlink, you can remove or install a chain on your bike in a matter of seconds.

That said, I rarely ever remove my chain to clean it. I just keep it well-oiled and wiped down. If you oil frequently and wipe it down, that seems to do a pretty good job of keeping your chain clean.