Go to your local discount store cleaning aisle and look for cleaners made for the insides of dishwashers. These provide ready solution to your worries and will get rid of any mineral build up. Cleaners which aim to clean metal and remove rust will be most helpful because mineral stains can build up to form rust as well. Get one and bring it home. Add it to your dishwasher soap dispenser and run a cycle with an empty wash. Read the use instructions on the package (normally at the back) for details.
If you want to use household products for the cleaning, you have a lot of options. White vinegar is known for its cleaning properties around the house from china to carpets. Take a cup of vinegar and use it to clean the dishwasher. You may also need to use an old tooth brush to remove the deposits manually.
Apart from vinegar, you can also use lemon juice. These solutions are high on acid content which helps remove the mineral stains from the washer. Doing this regularly, at least once a week will keep your washer free from all kinds of deposits, mineral and non-mineral.
Tang orange may not sound as the most appropriate cleaning product but it actually is when it comes to cleaning mineral stains. Make yourself a glass of cold tang and pour some in the soap dispenser of the dishwasher. The solution is high on citric acid and will work effectively against the stains.
As a general rule, run a free load of soapy water through the washer once you are done with the dishes. Do it daily or at least three times a week. After the soapy solution is flushed, run a load of clean water to rinse everything. Rub a clean damp cloth over the exterior surface of the washer to remove any dust and dirt accumulation.