First of all, let me mention the most basic tricks for the new traveler and then I will go into this trick that so few people use.
Booking cheap flights has always some basic points: always making the reservation at least 2 months in advance is one of them. Another one is avoiding the flights where a weekend is not included in the middle as they are classified as business flights and you will be charged more.
Other ones are avoid traveling in dates near to main holidays and specially avoid to book in days before or during main holiday periods. Instead, just after this holidays, you will find the best fares. Avoid also traveling in any flight that happens between 9:00 am and 5:00 pm as it is also considered business hours and you will be charged more.
Finally, within the basic tricks, it is the one that says that booking a round trip will always be cheaper than the same flights one by one, and also that a direct flight will normally be more expensive that an indirect flight, except if taxes in the airports are tremendous.
Going on with the hot stuff, let me tell you a couple of interesting things. How many times have you found into the situation that you have booked a flight and then suddenly the price has dropped so you felt a bit stupid for booking it when the price was high? And now another question: How many have you checked the price for your flight after you have booked it?
Well, probably the first thing has happened to most of the people reading, even if you don't know, because the answer to the second question will be generally a radical "No". And lots of times, and I include myself, we don't check this rates because we are afraid of feeling like fools when discovering that we could have got this ticket cheaper. We prefer to close the eyes and forget.
End of the story? No, it shouldn't be! If you want a good recommendation, I would definitely check the fares from time to time. If one day you discover that they have lowered the price and the amount is significant, the best thing you can do is to call directly the airline and explain the situation. Tell them that nobody told you it existed the possibility of getting this flight for a lower price, and it is unfair that they make you travel on this conditions.
Almost for sure they will refund you with the difference for the price. Airlines make big profits for all the people that do not check back the rates. And even better, if you politely ask for it, sometimes you can be given a free voucher for future ticket purchases with them!
Whatever you do, keep always in mind that, even if it is very common, the truth is the last thing you should be afraid of, as sometimes it can have a fair face even if you don't think so. And of course, it is always worth asking. The worst thing it can happen, as everybody knows, is that you stay the same.