First, you can rely on the search engines to do the initial search. Google Flights has become a go-to, as it lets you search by destination, date, and alternate airports and easily alter search variables. (It includes flights from most, but not all, airlines.)
After that, turn to a trio of similarly useful online tools, Skyscanner, JustFly, and Momondo. These websites focus on price first and are constantly updated.
After you find a fare you like, click or tap over to that airline’s website. You may be surprised to discover that the fare is even lower than what these search engines report.
If you are the type who likes to be on the lookout for a cheap fare, consider web portals like Airfarewatchdog and Scott’s Cheap Flights.
Lastly, think about following an air carrier or two on social media – another avenue through which an airline can suddenly unveil a good deal.