Planning your flights is one of the most complex things to do in planning your travels. If you are lucky enough that cost is not an issue, then there is probably no need to read any further. However, if you are like me and are out to find that deal, then keep reading. From the August 21st post, I mentioned some things that help in finding good prices for airfare. Now "good" is a relative term because it really depends on where you are flying to and how convenient you want things to be. Travel between certain cities where there is little to no competition can have ridiculously high fares especially if you live in a hub city for an airline. It's not fair, but that is how the airlines make their money when they sell $200 roundtrips between the west coast and east coast on a regular basis. The time of year you are wanting to fly also affects the prices. Do some searching on the high and low seasons for vacation destinations.
Back to the August 21st post. I recommended that you sign up for airlines' email lists and facebook pages. Many of the airlines including United and American have weekly deals that are released on Tuesday (usually) and the fares are good for the next few weekends. Some of these can be really great deals. I've seen deals from LAX to HNL (Honolulu) for less than $300. Of course these are for last minute travel so it might not be so helpful. I also recommended that if you see airfare that you know is a deal/steal, then book it immediately. It could be a mistake by the website or airline or a genuine rock bottom sale. Who cares why it's so low, just book it. In order to avoid losing any fare that you see as acceptable, I would do some planning before you seriously start looking for airfare especially international travel. I think the best thing you can do is to make a chart or matrix or a list of several different possible travel dates. For every big vacation I ever plan I have many pieces of paper with airline codes, dates, and prices all over the place. I do this so that I can explore all my options and there will be lots of the them if you have a choice of airports to fly in/out of for instance in Southern California there is a choice of at least 5 different airports with lots of air service. Many cities across the US and the world have multiple airports for their city. Usually one will be the major international one and then others will be domestic, but not always. Lots of travelers have no idea about this. Just do a general google search for a city and an airport. Surprisingly wikipedia or wikitravel can be very helpful for this. The latter choice is one that I use all the time.
For your initial searching, I would look at several different sites like: kayak, vayama, yapta, expedia, and orbitz. I rarely ever book from these sites but it's a place to start. Many of them will also let you set up "airfare watches" and it will look up prices on a route that you specify and watch to see if the price changes then email you. I rarely find good deals this way, but you never know. I really like kayak.com right now because there lots of ways to search. There was an article on msnbc about kayak and that it will "hack" a price by finding one-way prices that result in a lower roundtrip total price. It may require two bookings, but if the savings is substantial, then it is worth it. I think that having all of your flights on one nice itinerary is a thing of the past especially now that everything is electronic. Once I find options that I like on some of the above searching sites, I go to the specific airline's site to see that I can find the same fares. Sometimes they are even better on the airline's own website. On a few occasions I have booked flights on expedia because the fares weren't available on the airline's website or they were able to put together itineraries that included different legs on different airlines that aren't alliance partners. Another good thing that many people like about sites like expedia is that you can add hotel rooms to your flights and usually save money. I don't like to do this because by booking hotels through sites other than their own company's website, you won't get points/credit for your stay. If that's not a concern for you, then by all means book your hotel along with airfare.
One of the tricks in finding good airfare is looking for open-jaw itineraries. For example you fly SNA (Orange County) to EWR (Newark) and return JFK (New York) back to SNA (Orange County). Another open-jaw itinerary could be SNA (Orange County) to CMH (Columbus) but return to ONT (Ontario, CA).