Modern china can be easily washed in the dishwasher. But keep in mind that the hand painted, metal trimmed and antique china requires extra care while washing up. Don’t ever use hot water and a strong dishwasher for cleaning up the antique china as well as hand painted ones. This is because the hot water can greatly hamper the work done on such stuff. So better avoid it. Just mildly wash them with your hand. Do not wash your crockery pieces on daily basis as they may get fade away.
Mind it, black marks may show up on your china or other white dishes, if aluminum utensils including foil ones are mistakenly rubbed against these china while washing. Load dishwasher in such a manner that aluminum do not touch any of your china while washing process. You can buy plastic scouring pad and a mild abrasive cleaner from commercial store and use them mildly for washing purpose. Proper usage of both these items is very effective in removing the various marks that may have got appeared on your china.
Apart from cleaning, do not ever use the abrasive powders for any other purpose as the can remove the metallic or other decorations from your china.
For removing the tea stains from your cup, pour two teaspoon of chlorine bleach into 1/4th cup of water and use this solution. Just soak your china or white dishes into this solution for a minute or two and then rinse promptly. though this solution is quite effective in removing stains but even if this do not work for you, go for a commercial product for getting rid of stains from your dishes.