The most important tip I have seen for finding the lowest airfare is to purchase airline tickets in advance. In one specific example, airline tickets purchased with no advance reservation cost $515 dollars. Purchasing the tickets 7 days in advance dropped the price to $195. With a 14 day advance purchase, the tickets dropped to $120 dollars. So, a 14 day or more advance purchase of these airline tickets would save $395 dollars. Often you can find 21 day advance purchases which will save even more. So it would usually be a good idea to plan your travel in advance if possible.
Another suggestion is to be flexible. Perhaps you can book your departure flight out of a smaller airport. The smaller, less expensive airlines often fly from the smaller airports, and so you can get better prices on airline tickets than a major carrier flying out of the big airports. Also, the bigger airlines that do fly out of the smaller airports have to drop the prices on their airline tickets to remain competitive with the smaller airlines, which would save you money.
You also might reconsider your destination airport. For example if you are traveling to Los Angeles, you could see if the airline tickets would be lower going to the Burbank airport instead of LAX. You may have to drive a little farther at your destination, but the difference in price could more than make up for that. The less popular flights occur in mid-morning and late evening, and often have better prices than the more popular flights. So if you change your departure time, you can save yourself some money on airline tickets. If you can, plan to fly on Tuesday, Wednesday, or Saturday, as these flights tend to be less popular. And try to stay on Saturday night at your destination, as often airlines will offer lower prices on airline tickets.
Look into round trip airline tickets instead of one way. Airlines often charge less for the round trip tickets. Instead of flying from point A to point B, you may see if the airline tickets would be cheaper going from point A to point C to point B. So look into splitting the fares up like this. In a highly competitive market, prices on airline tickets can often change rapidly, so keep an eye on them.