Nudeyorker's advice is rather good. However, for the absolute cheapest prices on the web you must be prepared to sit in the middle seat in the middle row on long-haul passenger jets. For some reason Asians prefer the last couple of rows on long-haul jets; probably because there is no great competition for them, little Asian women can often sprawl out across three seats, and they are close to three restrooms. I'm not being racist. I'm being observant. Asians traveling to South America, Manhattan, and Europe must suffer much longer flights than those living in Europe and the USA atlantic traffic. Therefore, little Asian women are smart -- and frugal.
Remember, there are three classes of travel on the same plane: business/1st class, economy, and tourist. The difference between economy and tourist doesn't always mean the same thing on all airlines. Some Tourist tickets can be upgraded with sky miles. Most can't. Same goes for Economy. If you discover you have U or Y on your ticket, they can also SOMETIMES be upgraded with sky miles -- sometimes.
There is a third type of flight class you'll only find through a good travel agent and that is charter. Sometimes Internet sites such as Cheaptickets or Orbits may have a real inexpensive ticket that includes all country of origin and airport taxes to Germany or Moscow for an unbelievable low price. Most likely it's a charter ticket. These are usually the few seats a travel club, church group, or some other organization needs to fill to cover their costs of chartering a jet. However, you are at the mercy of a charter flight. You can only leave and return on the days noted on the ticket. No exchanges. No returns. And greater chance of having your luggage messed with. And the company flying the charter flight often doesn't recognize the flight in their computer because the codes don't match. But examples of good charter ticket are those offered through your credit card. American Express is the master of the chartered flight. That's why, during the middle of winter you can only fly to Cancun, Cabo San Lucas, Cozumel, or some Caribbean spot for 2 days and 3 nights, or some odd short period.
Edit: A word about American Express. I live and die by the AmEx. And rather than the old Green Card which costs a whopping $55 a year to carry in your wallet, they offer a variety of card products that issue sky miles good on almost all airlines willing to accept them. It might be worth checking their products and seeing if there is one that might be a good fit for your wallet. I've got so many ski miles on a Delta American Express Card that I'll never use them all (primarily, because they're hooked in with Delta). But years before there was such a thing as a Delta Sky Miles Card, American Express got me out of San Salvador, the capital of the tiny country of El Salvador, in the middle of a full-blown civil war in the middle of the night and to safety in Mexico City. So, check them out. They have some amazing insurance programs for lost luggage and their car rental discounts (which regularly change from rental company to rental company) cannot be undersold by any competitor. Plus, they are nice.
Another option is sign up for every airline travel club. They also know that an unsold seat is a seat they will never get to sell again. So, Wednesdays you'll often receive a ton of "cheap seats" for the following Thursday or Friday. However, you must be as flexible as Cirque du Soleil regarding departure, arrival, and return times. And if you go this option, joining airline frequent flier clubs, you'll suddenly become an expert on which airlines have the best service. And if you're a citizen of the USA you quickly learn that US Airlines are among the worst in the world. So far the very best service I've enjoyed -- sitting in economy -- is on LAN Chile (they treat everyone as if they are in first class, except you don't get silver-flashed flatware, linen, glass water and wine glasses, and extra wide sleeper seats). You do, however, get all the wine and liquor you can consume, and they are happy to sedate you with alcohol if it's going to be a long flight. And currently (unlike US carriers) you get everything else and do not have to pay for extra baggage. Second best is Korea Airlines which still flies a fairly new fleet of 747s and offers the calmest and most beautifully appointed equipment that lumbers through the air. Both LAN and LAX fly out of LAX. LAN may fly out of Kennedy. Both have major discount programs to keep every seat of their equipment full. However, you'll soon realize that a center seat in the middle row of a 777 or 747 is a bit more spacious on British Airways than the same seat and same row on the same Delta equipment. British Airways is having some difficult economic times. They aren't as fabu as they were two years ago. You'll also become a connoisseur of why Airbus is giving Boeing a run for it's engineering money. An Airbus300 doesn't look much larger than a Boeing 737 (although, it's substantially larger) and the width of the plane means wider seats. It can also glide you in extra comfort from Kennedy to Lima, Peru, something 737s were not intended to do. However, somehow Boeing is making those chubby 373s fly much farther than they ever have before. I wouldn't be surprised the next generation of 737s make it from Kennedy to Dublin.
Also remember that to keep your sky miles you usually must fly at least once a year, round trip, on the airline of the frequent flier club to keep your sky miles from turning back in to thin air.
Sadly, primarily because of economics, air travel has sort of reached what I call a lumbering speed and the great days of getting from here to there takes longer and longer. High output jet engines burn up more fuel and at a faster rate. So, the days of climbing aboard a Boeing 727-200 and making it from Denver to San Francisco in 1.3 hours is a long fading memory. And those 727s are still revered by retired passenger pilots as the sports cars of commercial airlines.
Remember that all new air equipment, regardless of manufacturer, is going to level off at a calibrated speed of a general 535 mph (or what ever that is in aeronautical knots). Airline equipment is better engineered for safety and efficiency, but back in the days when such considerations were figured with a slide rule, aeronautic engineers were no slouches. This is important if you've decided you'd rather be stuck on a large commercial jet for a 12-hour nonstop flight or prefer to break up your travel with several shorter flights. If you're old (like me) if may be a better deal for you to take "milk run" flights (flights of two or more to get to the same place) rather and suck it up and suffer through 12 hours of butt fatigue. Veinous thrombosis is a real problem for many people. More, but shorter, flights means you're forced to get up and move around; often changing planes in odd places in the middle of the night. there is another plus to this sort of travel: multiple flight itineraries are often cheaper. However, more than three changes in flight equipment to get from A to B is being taken advantage of. Also, I've lost count of the number of times I've had to change planes at Kennedy only to continue the exact same flight at Laguardia. Therefore, hold on to your ticket stub and be firm, but pleasant, when insisting for greyline ticket to the other airport and your airline refuses to arrange for ground transportation between two airports with the same flight number. One good thing to remember (while smiling and being nice) is to mention that this is something that will definitely be a highlight of the travel article writing. But don't use that excuse too much. I am a travel writer and have often been asked to produce legitimate credentials. But, if the connecting flight has the same flight number, by law it is the same flight. Again, be persistent (but nice). Delta and American are especially guilty of this. However, Delta is much more accommodating that American.
Know your airports. Texas still has a problem of flying you from Austin to Houston Hobby (domestic flights) letting you figure out on your own that you need to get to Houston International to continue on that vacation flight to Cancun (the airports are 40 miles apart). So be aware there is a commuter flight between the airports and that you have a reserved seat to get you to one airport to the other. Better yet, find a flight that leaves and enters the USA in San Antonio if you're headed to Mexico/Central America.
Never forget that, when checking in, the airline is keeping a record of you and that includes your behavior. Now you know why they have to do so much typing as they check you in, especially when flying to and from international airports. You'll soon notice that the same airline personnel who check you in and issued you luggage tickets is also the same flight personnel who will be serving you and tending to your precious little needs. I can't count how many times I've been bumped to 1st/business class at the last minute while standing in the tail section of a foreign carrier simply because I stayed out of everyone's way, commiserated and joked with the flight crew, and one time even offered to take another flight (knowing full well my baggage was already on board and they had to sit me somewhere). That's when that 1st class ticket magically appears. It also helps that you're not dressed in sweat pants and shirt that advertises that you're spending your grandchildren's inheritance.
And if you absolutely HAVE to fly on United Airlines, you have my sympathy. The friendly skies of United quit being friendly September 22nd, 1985 at 7:24 PM Pacific Time. And they didn't even have the courtesy to send out a memo!
¡Bien viaje!