If you want to find dirt cheap airline tickets, they are best found first by looking well in advance of your travel date; though of course the odd last minute opportunity is available - but that's more typical of vacation packages. Generally the earlier you book, the greater you chances of getting a discount airfare.
Low priced airfares are also very easy to get nowadays with the power of the internet. No more having to rely on a travel agent...the internet empowers you to find the best air fares by giving you direct access to the best priced plane tickets offered around the world. Europe has a bunch of discount airlines offering low ticket prices; and now asia does as well. Flights from bangkok to phuket in thailand, for example, can be had for just $40. Cheap airfares can also be found in the americas of course, especially in the United States. Its harder to find low cost airfares in canada and the rest of the americas - although mexico has also seen new budget airlines start up - Azteca Airlines, Volaris, and Interjet offer quite cheap airfares. In south america discounted fares are harder to find.
One problem with really cheap airline tickets is that you often have to pay for silly things like luggage; and may not even have an assigned seat. This is especially common with european discount airlines.
People often take charters to save money; but the discount airfare comes with a price, as sometimes their flights are unreliable. Its a pretty common experience to spend a few hours sitting in an airport somewhere; idling away because your charter flight is delayed. But the majority of flights are hassle free for most charter airlines. Just check into the company (google it) before paying for those cheap airline tickets. Have a great trip.