Use the dishwasher only as a last resort and only for cleaning solid wine glasses (never crystal glasses). Be sure to use a delicate wash cycle, avoid the heat drying cycle, and separate the glasses so they don't clink together. However, since dishwashers tend to leave some residue, you'll get better results in the long run by washing by hand.
Wash your wine glasses promptly, inside and out, after use. Remove any residue, stains, wine remnants, lipstick marks, or fingerprints. However, if washing your wine glasses immediately isn't possible, fill them with water to prevent the wine from sticking, making cleaning easier. Then, dry the glasses immediately with a clean microfiber cloth to prevent watermarks.