Many experts agree that one of the cheapest days to fly consistently, is Tuesday. Round trips starting and returning on Tuesday can be very affordable; of course, avoid holidays or long weekends that include Tuesday or are near a particular Tuesday. Wednesdays can also be favorable. On the whole, January and February tend to be the cheapest months of the year to fly.
Another way to determine how to find a cheap flight is to consider using Bing Travel, which actually offers a feature called FareCast that claims to be able to predict airline prices. Using various machine learning algorithms, an indicator appears for flights between major cities telling you whether the price is likely to rise, hold steady, or drop -- thus telling you whether to buy now or wait.