There are some sites like www.cheapflights.co.uk & www.skyscanner.net where you can get some idea but I haven't found them very satisfactory except as a rough guide. Quite often too the cheapest flights are indirect and can take up to twice as long as a direct flight.
The low season is always cheapest of course so if you establish that period for the place you are going to it narrows your search dates down. Of course the low season may also mean it is cold - or, if tropical, extremely wet.
I have found that I need to establish a time of year and then just slog my way through the main sites. Lastminute.com is a useful site now that you can tick the flexible date box & also look at direct only or all flights. It is easy enough to find the cheapest flights over a 4-6 week period for instance.
Perhaps the easiest way is to phone & put it in the hands of Travelbag or Travelmood or Trailblazers - the specialist long distance companies.