Once you have found a date, you can use the Internet to
Not only does it help to be flexible with dates and destinations but being flexible with the route you take is another way to get a cheap flight. Sometimes it’s cheaper to fly to London and take a budget airline to Amsterdam than to fly direct to Amsterdam. There are so many budget carriers around the world that taking advantage of a good deal to another city and then hopping on a budget flight to your destination is sometimes the best way to go. I had to go to Paris once; the flight was $900 USD, but I could fly to Dublin for $600 and get a $60 flight to Paris. It meant more flying time, but the $240 I saved was worth it.
If a new resort opens, they may offer cheap airline tickets
While the above search engines are great, they do not always include small airlines, especially in less popularly booked routes and/or in remote regions. If you're flying somewhere obscure, Google search and ask around if there exists a local airline. While in South America we learnt that the LADE Air in Argentina (run by the military) has cheap flights to Patagonia, which is of course not listed in mass search engines online.
Although online travel websites are a great way to find cheap travel rates, you will want to checkout the airlines themselves. All airlines have online websites. Many will regularly offer deals and discounts on many of their flights. These deals and discounts are likely to change often, so if you see something that catches your eye, you may want to snatch up the deal real quick before it is gone.
Fare comparison sites are usually the first stop for people