What Makes Fish Kosher?

The Torah says that for fish to be Kosher they have to have fins and scales but what exactly are the scales that make a fish Kosher? Do fish that drop their scales or have a handful of scales count as kosher? What about fillet where the skin has been removed? How can we know if the fillet is kosher?  A fascinating discussion about what makes fish kosher and how we can identify kosher fish.