My recommendations regarding the purchase of the Flight Ticket :

I am flying quite a lot.  You can read information about my trips on my sites about : Vietnam, Thailand, Barcelona, Tel-Aviv and Jerusalem.
Here is how I search for a flight :
To find International flights, I recommend to use Skyscanner. It has an excellent user interface and good prices. Especially useful is the option to see the cheapest price within a month (If you are flexible with the dates).
Here is how to use Skyscanner :

1. 1. Choose your preferred language and currency, on the top right part of the page.
   2. Fill your destination and dates (check “one way” if you want), then click the “Search Flights” button.

1. You will see the search results. If you are flexible with the dates,  then click the “show whole month” link on the left top side of the page. It will show you a calendar (and a chart) with the cheapest price available for each day.

When you choose a flight, consider also :

• The landing time (at night, it may require a Taxi instead of public transportation)
• The connection wait time (if you need to change airplanes)
• The airports location (some airlines are not landing at the main airports)

Notes :

• Skyscanner is a search engine. It doesn’t sell you the tickets.
  It points you to companies who do sell tickets (like a specific airline).
• The price you see on a search engine, is not always the final one (although they try hard to be accurate). Sometimes there will be extra fees like for suitcases or taxes. So in order to know the final price, you must advance in the reservation process.

Advanced options, if you are energetic :

• Search engines like Skyscanner are good and they give you a good picture of the available options, but sometimes, for many reasons, they don’t show you all the available flights (a minority may escape). So try to look also at individual sites of the companies you know that are flying to your destination. In order to know the airlines who are flying to your destination, you can try to look at the “departure and landing real time information” of the airports sites.
• Other search engines for flights that have a great user interface : Google flights and Momondo.

When is the best time to buy a flight ticket ?

Usually, the sooner, the better (something like 2 months in advance). It is especially true with the “low cost” companies (these ones are almost always flying at full capacity). There are also deals of the “last minute” but you cannot really count on it if your destination and schedule is not flexible.
Thankfully, air travel as become very competitive and you can usually find good prices to your destination, at any time, if you are willing to make a non direct flight.