Since most fares have advance purchase requirements, the best fares exist more than 21 days before your travel date. However, if this is too soon, book your ticket at least 14 days in advance to get the best deal.
A slight change in your itinerary can reduce ticket prices. Fares are typically lower on low demand days and times (Tuesday, Wednesday, Saturday and late-evenings). Not only will you save you a lot, but you may also 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 round-trip ticket is often priced less than two one-way trips and is sometimes priced less than a one-way trip. Unless you are certain you are not coming back, book a round-trip 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.
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 may change minute-to-minute. If you see a fare that works, book it because it might not be there two minutes later.
Flight with connections are usually cheaper than nonstops. 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.