The Iguazu Falls are split across Brazil and Argentina. I was visiting from the Argentinian side, but wanted to see the Brazilian side as well. It's quite a hassle to do as just a day trip, but I guess that's my style.
As an American, you need a not-so-cheap visa to visit Brazil. Although it does last for 10 years, getting it for a day trip is admittedly kinda pricey. If you're in the Bay Area, make sure to plan well in advance as getting an appointment at the Brazilian consulate generally requires a date several weeks out.
Having worked out the paperwork, I ended up hiring a taxi driver for the day. From Puerto Iguazu in Argentina there was enough time to cross into Brazil and straight on to Ciudad del Este in Paraguay for an hour or so before hopping back to Brazil to see the falls. Shortly after crossing through Argentine immigration, you'll drive over the Iguazu River, offering just a very small glimmer of a hint of what's to come.
View of the Iguazu River prior to it reaching the Iguazu Falls.