How do you clean parts?

[R Leo]

Since these cars are old enough to have accretions of crud that seem to alter the appearance of some parts and oil leaks that make the Exxon Valdez look like a drip, I'm just curious to find out how others on the forum go after this noisome task. Red rags? Disposable shop towels? Parts washer? Dishwasher? Kitchen sink?

And, while we're at it, how clean is clean? Enquiring minds want to know!