The invention of the dishwasher has made cleaning dishes easier, but they're not great at drying dishes well and often leave your dishes with a damp film.
Instead, place a hand towel (preferably made of terry cloth) halfway inside the dishwasher once the wash cycle is complete, letting the other half hang out.
Just make sure to close the dishwasher with the towel half inside so it can get to work absorbing most of the steam. The result will be damp-free dishes.