Travel agents
Domestic tickets can be purchased from travel agents and travel agent websites. Travel agents often work together with airlines to offer discount air tickets. Travel agents also work with hotels and restaurants and have great holiday packages. Purchasing your flights this way may actually work out to be less than what is offered by the airlines themselves.
International
A round the world ticket enables you to fly around the world for a discount price. You can get very cheap round the world student tickets. Tickets are generally around $300-$5000 for 5 or more stops. Backtracking is restricted and you usually have to go in one direction. An alternative to the round the world ticket is the continent pass. For a low price you can travel freely using all continental flights. There are a number of flights you are limited to and price varies. But ultimately with a continental pass you will benefit from networks of airlines.
It is cheaper to book your flight online and you can generally also get great discount air tickets during off-seasons.
Domestic
If you travel regularly on domestic flights you should sign up to the airlines email services. Airline companies will then be able to keep you up to date on their deals. That way hen a great deal comes you'll be first to take advantage.