Run your coffee maker through a full cycle using three parts vinegar to one part water. This will clean out not only the coffee stains in the part of the maker you can see but also mineral deposits and buildup in the hoses of the machine.
Dip an old toothbrush in the coffeepot to get it damp then dip it in baking soda. The vinegar from the coffeepot will combine with the baking soda to create a powerful and gentle deep cleaning abrasive. Use this to brush gaskets and crevices to remove coffee stains that have been loosened up by the vinegar steam and heat.
Wipe everything clean with a sponge and remove any debris that you brushed out.
Dump the vinegar from the coffeepot and refill with plain water. Run the coffee maker two to three times to rinse all the vinegar and baking soda from the machine and parts.
Wipe all pieces of the coffee maker with a small dish towel to dry. Your coffee pot, basket and gaskets should all be clean and free of coffee stains.