The ITA Matrix is a great and free tool to find the flights you want since it can:
– search flexible dates
– almost all airlines in the world (but not most discount airlines – for these use wegolo.com)
– can search only specific airlines due it's advanced routing language
– search nearby airports
The departure and arrival airports are needed first. Then select 'See calendar of lowest fares' and a flexible number of nights. I usually set it to 3-7 since many fares may require a 7 day stay it's a good idea to use these defaults.
I also set the currency to USD – this is not required but is a good habit if you search fares from other places outside the US.
Once the search is done you will be presented with a calendar that shows the best price per day.
A click on a day reveals the fares per day.
Note that you can't book any tickets at ITA Matrix directly so note down the exact flight dates and destinations and book via Expedia, Orbitz or Cheaptickets. At least one of the sites should show you the exact same result.
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2) Flexible search with dates +/- 2 days
While 30 days flexibility might be great – the search engine may overlook results that might be even better (but more complex to build) so if you are not as flexible use the +/- 2 day search instead.
3) Nearby airports
The best prices are often not available from your closest airport but from nearby airports. ITA Matrix offers the ability to use nearby airports within a wide radius.
4) Search only one airline
Under certain circumstances (i.e. a double mileage credit promotion) it might be a good idea just to search one airline. No problem with ITA Matrix.
All you need is the airlines IATA code which you can look up here.
Open the field for 'Advanced Routing codes' and enter the IATA code followed (no spaces) by a '+'.
The results list will then only show the airline you specified.