Buy your tickets early. Rick Seaney, CEO of Fare Compare, recommends purchasing tickets three to four months prior to your departure date, if at all possible. At this time frame airlines tend to feature the lowest prices.
Purchase tickets in the middle of the week, especially on Tuesday afternoons --- that's when they are the least expensive, according to Rick Seaney.
Apply flexibility to your travel. Avoid Saturday or Sunday departures; leave a day or two earlier or later. According to travel site FareCompare, Wednesday is historically the cheapest departure/return day.
Check with nearby airports when booking your flights. Sometimes your flight is less expensive if you fly to an airport near the one you originally had in mind. For example, if you are flying to Los Angeles, compare the price at LAX to nearby John Wayne Airport in Orange County; sometimes seats into or out of John Wayne are less expensive.
Check the airline websites in addition to travel websites. While travel websites allow you to compare fares on multiple airlines in one search, they don't always feature flights from airlines such as Southwest. Sometimes you'll find less expensive tickets by purchasing directly from the airline.