Photo by Dennis Matheson.
We've discussed one way to clean cloudy drinking glasses before, but for a bit less work, you can get similar results with the seemingly magic all-purpose vinegar:
A simple dish rag or towel with a few tablespoons of white vinegar on it is all you need to clean things up. It will evaporate and leave you without any taste, but if you're still worried you can fill a shallow pan or plastic dish tub with hot water and add 2 cups of vinegar to it. Give things a soak, shake off excess water and let sit to dry.
In certain cases, you could even throw some vinegar in you dishwasher's rinse compartment, though that won't give you as strong a cleaning if your water's especially hard. Hit the link to read more.