The first thing you want to do is take out the carafe and get it squeaky clean. This can be accomplished by using soapy water in the sink or by just using the dish washer if you own one.

For stubborn, burnt-on residue, try using a Scotch-Brite blue scouring pad and warm soapy water. An legendary waitress trick is to fill the carafe with ice cubes and swirl them around for ten minutes. No kidding, it works -- sometimes.