My method:

1. Check kayak.com and sort based on flexibility. The more flexible you are, the cheaper you can find the flights.

2. Check the wiki page for the airport I'm flying into. Cross check which of those airlines are listed on Kayak (I have this pretty much down) and any others on WhichBudget.

2. Starting with the ones not listed on Kayak or WhichBudget, check their websites. My level of dedication to getting a cheaper fare would dictate how many of those flights I would take.

3. Know that it's usually cheaper when flying between Europe, Asia and Africa to fly through the Middle East. It's also almost always cheaper to fly through CDG, LHR, AMS, FRA or SVO and get a budget flight to that location from where you are.

Of course this is international. I don't have much experience flying domestic.