The USA has more than 375 domestic airports, but only a baker's dozen are the main international gateways. Many other airports are called 'international' but may have only a few flights from other countries – typically Mexico or Canada. Even travel to an international gateway sometimes requires a connection in another gateway city (eg London–Los Angeles flights may involve transferring in Houston).
International gateway airports in the USA:
Logan International Airport (Boston; www.massport.com/logan)
O'Hare International Airport (Chicago; www.ohare.com)
Flying midweek and in the off-season (usually fall to spring, excluding holidays) is always less expensive, but fare wars can start any time. To ensure you've found the cheapest possible ticket for the flight you want, check every angle: compare several online travel booking sites with the airline's own website. Engage a living, breathing travel agent if your itinerary is complex.
Keep in mind your entire itinerary. Some deals for travel within the USA can only be purchased overseas in conjunction with an international air ticket, or you may get discounts for booking air and car rental together. Or you may find domestic flights within the USA are less expensive when added on to your international airfare.
The big three US travel-booking websites are Travelocity, Orbitz and Expedia. Similar to these and worth trying are Cheap Tickets and Lowest Fare. Typically, these sites don't include budget airlines such as Southwest.