Ice In Water Line to Ice Maker

The ice maker is not making any ice. The feed tube in the very back of the ice maker appears to be clogged with ice. On the back of the refrigerator is a water line inside of a rectangular piece of plastic. It appears to lead directly into the feed tube. How do I remove the feed tube so that I can get the ice out of it? I would think that I have to clear the line before I fix any additional components (such as the switch at the bottom of the refrigerator which activates water flow). I thought about turning the refrigerator off but then I might ruin the contents of the freezer. Also once I get the tube out of the refrigerator what is the best way to clean out the tube? Hold it under warm water? Please advise.