Clean the entire coffee maker. If you see stains on the carafe, there are bound to be stains on the inside of the machine.
Wet a sponge and put a drop or two of detergent on it. Squish it around until the detergent goes into the sponge. Squeeze the sponge until it's almost dry. Wipe down all parts of the coffee maker, inside and out. This will remove any coffee oils -- these carry the coffee flavor, but they can coat the carafe and become rancid, making the next pot you brew taste nasty. Wet a paper towel with plain water and wipe again to remove any detergent.
Add white vinegar to the carafe until it's half-full. Then fill it with water all the way to the top. Let this sit for 15 to 20 minutes. The acid in the vinegar will react with the mineral deposits, clouding your carafe and loosening them.
Put a paper filter in the basket, pour the vinegar-and-water solution into the tank, set the carafe in its normal position and turn the machine on. When it finishes brewing, pour out the vinegar solution. Remove the used filter and replace it with a new one. Fill the carafe with plain water, pour it into the tank and brew again. When it's done, smell the water in the carafe. If you can still smell vinegar, pour it out, let the coffee maker cool for 15 minutes and run another pot of water through it. If you still smell vinegar, keep doing this until you no longer smell it.
Scrub the inside of the carafe gently with a plastic scrubber if it is still brown or cloudy and fill it again with half vinegar and half water. Let it sit again for 15 to 20 minutes. Scrubbing will remove the top layer of sediment loosened from the first soaking and let the acid in the vinegar attack the next layer. Repeat until the carafe is clean and clear.
Wash the carafe thoroughly with warm water and detergent, rinse it carefully and dry it with a paper towel inside and out so there will be no new mineral deposits from air-dried water droplets. The next pot of coffee you brew should taste much better.