Dirt cheap airline tickets are easy to get. The first step is to book early! Even though this seems obvious, many people wait and wait thinking they are going to get better deals. In some cases this may be happen, but the first tickets to be released are usually the cheapest. The airlines even have a specific day and time when they release these new tickets. If possible book at least 1 month in advance. So you've got less than a month to find dirt cheap airline tickets? Don't worry, airlines still often offer significant savings up to a week before flights.
After that...you are on your own. Since businesses purchase tickets between 9am and 5pm don't book during this time! Airlines love to bump prices up to gobble up all they can get from businesses, and unsuspecting deal seekers! If possible book your flight over a weekend. Airlines think that business people rarely stay over weekends so again, they jack up the price. This 'trick' recently saved me $92 bucks on a round trip ticket to New Orleans by staying an extra day. Avoid flying on Mondays and Fridays. This is the busiest day and thus, the most expensive. Save money and bypass long lines by avoiding these days. Fly on Tuesdays and Wednesdays, these are the cheapest days. Many airlines have promotions right after major holidays to try to keep sales up.
You can profit off this by waiting until after holidays to find some dirt cheap airline tickets. Certain airlines offer discounts for certain groups of people. If you are a clergyman you can often get a reduced rate with clergy identification card. If you are in the military you can often get reduced rate as well. Often many people buy airline tickets "from the source" without going through a middle man. Middle man AKA travel agents are just another step between you and the ticket, jacking up the price...right? WRONG. Always consider buying from a travel agent! Why? Because they get special discounts from the airlines that are not allowed to the public.