Be flexible in your travel plans in order to get the lowest fare. The best deals may be limited to travel on certain days of the week (often Tuesday through Thursday, or Friday night through Sunday morning) or particular hours of the day (e.g., late-night departures). This applies to each of your flights, not just the first flight in your itinerary. After you get a fare quote, ask the reservations agent if you could save even more by flying a day earlier or later, or by taking a different flight on the same day. Or simply ask the agent what the lowest fare is, and what you need to do to qualify for it.
Discount seats are usually "blacked out" during holiday periods. However, you might be able to get a discount fare if you fly on the holiday itself (e.g., New Year's day).
Plan as far ahead as you can. Most airlines set aside only a few seats on many desirable flights at the lower rates. The real best bargains often sell out very quickly. On the other hand, if a particular flight is not selling as well as expected, air carriers sometimes make more discount seats available for a particular flight just before the advance-purchase deadline expires. For example, if the lowest fare has a 21-day advance-purchase requirement but is sold out for most dates, and you can go any time, ask about fare availability on flights 21 or 22 days from when you call.
While planning ahead is a good general rule, if you can bide your time you might encounter a "fare sale." Many airlines put seats on sale for brief periods several times a year (although you usually can purchase tickets for flights weeks or months after the end of the sale period). It is difficult to predict when these sales will occur, although they often fall during times when people are less likely to buy airline tickets (e.g. early autumn or right immediately after New Years).
In a large metropolitan area, the fare could depend on which airport you use. For example, if you are going to Southeast Florida and plan to rent a car, it might not make much difference if you fly to Miami or Ft. Lauderdale, except for ticket price. Also, a connection (change of planes) or a one-stop flight is sometimes cheaper than a nonstop. Always check on alternate airports and routings when pricing a ticket.
Look into all airlines that serve the market you are interested in, including low-cost carriers that offer low fares. Many times the major carriers will match the fares of a low-cost airline between the same cities; but often this will only be for a certain limited number of seats on each flight. On a low-cost carrier, find out what you get for your money: baggage transfers from one carrier to another, meals, advance seat assignments, etc. Note that small airlines sometimes have only one flight per day in many markets, and they frequently will not reroute you on another airline if your flight is canceled or delayed. In such cases you may have to wait until the next day to fly.
Ask about all restrictions on your fare. Typical requirements for discount fares include purchasing a round-trip ticket, buying the ticket a certain number of days before departure (e.g., for many fares, at least 14 or 21 days before you leave), purchasing the ticket within 24 hours of making a reservation, staying over a Saturday night, traveling during a certain time of the year, staying no more than 30 days, and, as discussed below, refund/change restrictions.
Ask about your ability to change or cancel your flight if you need to. Even if you get sick, you cannot assume you will get a refund. In fact, most discount tickets now are non-refundable, but can be applied toward the purchase of other tickets on the same carrier. You must usually pay an administrative charge and any difference between the fares for the old and new flights when you do this.
Consider using a travel agent. Agents usually do not charge a fee (they get a commission from the airline), and they can tell you about "consolidators" and other sources of discounted seats that are not available directly from the airline. However, consolidator seats can have even more severe restrictions than the airlines' own deep-discount fares, particularly if the flight is delayed or canceled. A few travel agents sometimes have access to special deals with a particular airline (either discounts or extra services). If you are flying to a popular foreign destination, or to Las Vegas or Hawaii, ask the travel agent about Public Charters. These charters sometimes offer lower fares, but again with significant restrictions that are spelled out in an operator/participant contract that you should review carefully.
Ask the travel agent if the city where you live or the city where you are going is an airline "hub." If it is, fares may be higher than for flights to other nearby cities because of reduced competition. Someone who lives at a hub might save money by leaving from another nearby city, even if they end up connecting through the hub to get to their destination.