As mentioned before, when the email came for a severely reduced price to fly one way to New Zealand for $400, I knew I had to take it. I have flown on about as many airlines as countries as I have visited, and believe me; they are not all created equal. That being said, I found a few ways to save some money while booking my flights, and here they are.
Sign up for discounted flight emails: I got my New Zealand ticket after I got an email from TheFlightDeal.com. I have been a subscriber for close to two years before I was able to use it. How it works is that someone knows the ins and outs of the ITA Flight Matrix and posts deals to locales from hubs inside the US. Since I had air miles with my most favorite airline, I took a domestic flight to a hub on my points, then picked up my international flight. Joining TheFlightDeal.com is easy as all you have to do is enter an email. Unless you have an absolute time you need to travel, this is the best way to get discounts.
Google Flights: Google Flights was my go-to for booking flights where I needed a hard entry date and hard exit date due to either Visa issues or just needing to move to my next stop. It scours most of the internet to find deals, then gives you options for travel and offers you a variety of ways to book. Create an account with Expedia, Orbitz, or other travel companies so that if they offer a deal through Google Flights, you get a twofer as you will get a cheap flight as well as points to use further along your journey.
ITA Flight Matrix: While this is still part of Google, the ITA Flight Matrix allows more customization. As mentioned above, TheFlightDeal.com uses it to find flights. It offers options for connections, airlines, and the like, so this is much more advanced that simply plugging in your desired details.
SkyScanner: I like this site because all you need to do is type in a country from which you will be departing and a country where you would like to go. It then offers you options from the very cheap (usually due to early hours, layovers, and connections) to the more reasonable.
Sometimes to make things much more accessible, download the app of the airline with which you will use. As mentioned before, developing countries use apps much more than they use laptop or desktop computers. For this reason, local airlines usually put much more research and development into their apps that their websites. They allow a more exceptional user experience, and most come with translations.
Pro-tip: If you need to fly somewhere that is a great distance, you can severely reduce the price of your flight by turning it into a multi-city flight on two or more different airlines, much like the domestic tip mentioned above. Find a hub that both your departure country flies to as well as your arrival country. Book a multi-city flight, flying from your departure country to the hub, then from the hub to the arrival country. Make sure you arrive and leave the hub on the same day, at least 4 hours apart to clear customs and retrieve your bag, if you have stowed luggage. You can save BIG money that way.
One final note, be sure you know when your flight leaves. I know it sounds elementary, but around the world, if a flight leaves at 01:00, that means it leaves at 1 in the morning, not 1 in the afternoon or 13:00. I had had a few WTF moments when I realized I booked a flight leaving an airport at 3 am.