If you are happy to put your bare hands into the water, your pottery should not come to much harm. Put a rubber mat in the sink - if you drop an item, it has a better chance of survival. It is a good idea to take off any rings that might scratch the pottery. To remove stains, soak the item in warm water for as long as it takes. Abrasive cloths or powders are not recommended because they damage the surface glaze, which is a thin coat of glass.
Unglazed items are particularly vulnerable.
The best way to dry pottery is to rinse it and let it 'drip dry'. Dishwashers Dishwashers are very convenient but, when you consider how they work, you may not want risk your fine pottery in this way. Dishwashers operate at very high temperatures and water is sprayed with force at the contents. Dishwasher cleaning fluids are abrasive and the powders are worse. Harmful proteins may build up on items that are washed regularly in a dishwasher.