OK, let's start with some basic questions before getting into the step-by-step guide.
Where will I save the most?
It’s not so much which destinations will save you the most money, but which airlines. For example, Norwegian Air is almost always significantly cheaper if you pay in Norwegian kroner. Same with Chilean-based LAN Airlines: pay in Chilean pesos, and you’ll save. Or LAN’s sister airline TAM has shown similar savings if you pay in Brazilian reais.
Do I have to fly to those countries to save?
No. The key is to pay in the national currency of wherever that airline is based. For example, a round-trip ticket from New York to Barcelona on Norwegian Air from March 23-30 is $891 if you pay in dollars, and $809 if you pay in kroner.
However, flying to the airline's country of origin will produce even bigger savings. For example, a round-trip LAN flight from Miami to Santiago from April 22-29 is $706 if you pay in dollars, and $599 in pesos.