I found this photo on Flickr, but I have the same coffee pot and the same dirty stove so it was obviously meant to be.
- Dump any old grounds out of the filter basket.
- Fill the carafe 1/3 full with white vinegar and the rest with water.
- Run the solution through the coffee maker, just like you're making a pot of coffee.
- Turn off the coffee maker and let everything cool down.
- Wipe out the carafe and water reservoir with a washcloth (you can use a little dish soap if it's really gunked up!).
- Run a full carafe of water through the coffee pot to rinse. Dump it out. Now do it again.
- Make coffee. Enjoy its smooth, un-mud-like flavor and aroma.
I like to clean out the coffee maker about once a month. You can do it as often as tickles your fancy. Before your coffee starts tasting like mud and gunk is ideal. ;)