The most convenient way to reach Foz do Iguaçu is to arrive at São Paulo airport (Guarulhos International Airport, GRU).
From Europe: Flight time from Europe to São Paulo is just over eleven hours depending on your starting point. Most flights leave from Europe in the evening and arrive in São Paulo early in the morning. On the return leg they leave late afternoon or early evening to get to Europe the following day around lunchtime or earlier.
Air France, Alitalia, British Airways, Iberia, KLM, Lufthansa, Swiss, TAM and TAP all run regular services between Europe and São Paulo. This means that travelers have a choice of several different airlines linking the two continents daily.
From the US: Flights by American Airlines, Continental, Delta, United and the Brazilian flag carrier TAM link the US with Brazil. Flight time is 8.5 hours from Miami to São Paulo, just over 9 hours from New York, 11 hours from Atlanta, 13 hours from Los Angeles and 16 hours from San Francisco. The vast majority of flights between North America and Brazil are overnight flights that arrive in Brazil in the early morning.
From Latin America: São Paulo receives daily flights from most of the major Latin American cities and is served by Aerolineas Argentinas, Avianca, Copa Airlines, Lan Chile, Taca, Pluna, and the Brazilian flag carrier TAM and GOL.
From Asia: São Paulo also receives daily flights from many cities in Asia; usually the flights are via Europe (e.g. Frankfurt, London, Amsterdam) or via US (e.g. Los Angeles or New York) and flight time depends on your starting point. The following companies make regular flights to/from São Paulo: JAL, Korean Airlines, Qatar Airways, Emirates, Air China, United Airlines, Lufthansa, Air France, KLM, Alitalia.
You can then fly from the same arriving airport in São Paulo (Guarulhos International Airport, GRU) or Rio de Janeiro International Airport (GIG) to Iguaçu Falls (see timetable below).