Since most fares have advance purchase requirements, the best fares exist more than 21 days before your travel date.
A slight change in your itinerary can reduce your ticket prices. Fares drop on low demand days and times (Tuesday, Wednesday, Saturday and late-evenings). Not only could you save a bundle of cash, you might even end up with the entire row to yourself!
Nearby airports may have lower gate fees, in which case the airlines pass the savings onto you. In addition, non-major airports can be less crowded and easier to get in and out of.
A return ticket is often priced less than two one-way trips and is sometimes priced even less than a one-way trip. Unless you are certain you are not coming back the same way you came, book a return flight.
Sometimes a lower fare is available if you stay over on a Saturday night. An extra night at your in-laws' house may raise your blood pressure, but will likely lower your fare and avoid the 'weekend away' crowd in the Friday night rush.
Holidays and school vacations are the highest-demand travel periods. Early planning improves your chance of finding the lowest fare or rate.
Booking a trip as a package makes searching easier and can be much cheaper than buying the components of the trip separately. Airlines and hotels will discount more if they can bury the reduced rates in a package.
When searching online, fares can change minute-to-minute, especially when sales are released with limited numbers of seats. If you see a fare that works, book it before someone else snaps it up first!
Flight with connections are usually cheaper than direct or "non-stop" flights. Some may dislike the hassle of a longer trip or the risk of missing a connection, but a few hours of extra travel may save you a lot -- and will give you a chance to stretch your legs.