The airfare system for domestic and international travel is very complex and is always based upon the airlines getting the maximum revenue possible.   There are some rules that may seem unintelligent, but the airlines spend millions of dollars researching travel patterns and they very well understand how to get the most travel dollars possible.   So for you to spend the least travel dollars possible, you should understand some of the reasoning and be flexible.  

Full fare tickets are expensive but have no restrictions and are very seldom purchased by the public.   Anything less than full fare will be called a restricted or discounted ticket which will include restrictions and penalties.    Airlines want to fill as many seats as possible, so they offer discounted tickets with associated penalties and restrictions but also offer the full fare tickets for those willing to pay for no restrictions.  

The following guidelines apply to both domestic and international travel but will usually be more consequential for international travel.  

• Plan Ahead and buy your tickets at least one month in advance.    Two to six months would be even better in many cases.  
• If multi segment flights are required, include as many as possible in the initial purchase.   If you wait for later to purchase a separate ticket, expect to pay more.     
• Don’t wait to purchase because you are not sure of your travel dates.    Usually the cost of changing the ticket to a different date will be cheaper than waiting to purchase later.  
• All flights should be for confirmed reservations before any payment is made.  
• It is easier to change the travel dates then it is to change the travel destinations.   Avoid Open tickets if possible.  
• Purchasing airfare directly from the airlines or through internet purchases without a travel agent may not be the best or cheapest method.    Not all flights and fares are listed on the internet, new airlines with the cheapest airfare may not be known to you and not all the rules or restrictions are well published on the internet.   Web fares can provide some good deals but are typically unpredictable and have restrictions on length of stay and travel times.     
• If using a travel agent or travel consultant, find one that specializes in your planned destination.   You should be using someone that has traveled to your destination at least once.   Travel agents seldom get a commission from the airlines, so they must charge a service fee, which means they are working for you.    It is usually best to use your time in finding the right travel agent instead of the time finding the lowest fare yourself.   With the internet, phone and email, you don’t need a local travel agent so you can expand your search.  
• To find a good travel agent, ask if they specialize in your destination and if they offer discounted tickets.    You can review their advertising and check their response to help qualify the agency.    Also does the agent seem like a salesperson or more of a consultant that is knowledgeable about your planned destination?     
• Roundtrip airfare is not always the cheapest.   In some cases where multi segment flights are required, especially within a single country and using the same airline, one-way tickets can be cheaper.  
• Advertised prices for discount tickets usually do not include taxes and fees.   There may also be some restrictions you just can not handle, so make sure you understand the rules.  
• Usually the airfare is geared to charge the business and long stay traveler the highest prices.   So if you stay over a weekend and less than one month, the airfare will be lower.  
• Purchase domestic tickets for other countries when buying the international airfare and you may be able to avoid the domestic taxes.  
• Pay attention to the direction of travel, airfare from point A to B can be higher than form point B to A.    So if you have a multi segment flight plan, being flexible can save you some money.  
• Least expensive days to travel are Monday to Thursday.    Departing flights on Friday to Sunday (sometimes Monday) will usually cost more.  
• Some obvious restrictions are nonrefundable, non changeable, use it or loose it, use within certain dates and limits on travel stays.   So know the restrictions and be flexible if possible.
• E-tickets have some disadvantages like non-assessable when the computer system is down, for some international travel paper tickets are required and paper tickets make it easer to change airlines if necessary.    However paper tickets can get lost.
• Purchase airfare with a credit card, which offers more protection.