While three days is more than enough time to see just the falls, there is more to Foz do Iguacu and the surrounding area that is worth exploring.
Day 1: Touchdown in Foz do Iguacu
Arrive in Foz do Iguacu and get settled in, perhaps grabbing a bite to eat at one of the city's excellent selection of restaurants. If you have time, it takes about three hours to explore the Brazilian side of the falls properly; enjoy! Photographers should note that vistas over Iguassu are prettier in the morning; consider visiting Parque das Aves (Bird's Park) instead, and saving the park for the a.m. Either way, be sure to book a 10-minute helicopter flight out over Garganta del Diablo, to appreciate the scale of this natural wonder from above.
Day 2: Off to Argentina
Though the panoramic views over the falls from the Brazilian side are by all accounts best, Argentina offers the immersion experience, with several kilometers of trails that thread the thunderous falls and crashing spray. Allow at least five hours to experience the Argentine side of the park, more if you have time. Return to Foz do Iguacu in time to enjoy the late afternoon light at the Hito Tres Fronteras (Three Borders Landmark) and do some souvenir shopping.
Day 3: Upstream to Itaipu Dam
Enough natural wonder? Book a half-day tour to Itaipu Dam, considered one of humanity's most impressive engineering marvels. If you're bound for the beaches bound, consider grabbing a bus (or booking a tour) to Santa Cruz do Sul and Catedral Sao Joao Batista. Spend the night in the pretty Colonial city before continuing on to any of several seaside destinations.