Photo by Admiller.
Redditor SandRider explains one of his favourite household tips:
If you have coffee or tea stains in your mug you just sprinkle a tiny bit of baking soda in there and just a little water — doesn’t even have to make a paste — wipe it around with a finger or sponge. Totally clean.
Supposedly, you can also use something like Tang that has lots of citric acid, or the ever-useful vinegar to do the same thing. Once you’ve got it clean, make sure you wash it regularly as soon as you’re done drinking to keep those stubborn stains from showing up again, too.