Three examples of cognitive dissonance might include a smoker who continues to smoke despite the knowledge that it damages health, a cult member who alters their beliefs when they are proven wrong and someone who cheats on a test once, but resolves never to do so again. In each case, the individual is attempting to resolve the tension created by behavior that goes against their beliefs.
In the example of the smoker or the cult member, it is the beliefs themselves which are altered to fit a new perception of reality. This is commonly called "rationalization." In the last instance of the cheater, the behavior itself was changed to adhere to beliefs..