It is very easy to get around Foz by public trasnportation if you stay at a hotel on Catararas Street (the road to the falls- hotels like Bourbon, Rafarain, Turrance Green, etc).   By bus from airport go to end of airport and take the bus that says Centro for $R2.65, it goes past all the hotels on Catararas, just pull the cord to stop at your hotel.  To get to the Brazil Falls, go to nearest bus stop (only 20 meters from any hotel on Catararas, look for bus that say "Nacional Iguacu" , (tyou need to raise your hand to get the bus to stop), the last stop is the falls, cost only $2.65.

To get to Argentina falls by public bus is also easy and will say you $80-150 if you do this versus the tours.  Go to the same side of the street as you did to get to the Brazil Falls, look for bright colored buss that say "Argentina" on it, cost $R4.  It will take you to the border, where everyone on the bus gets off and goes thru a hallway to get their passport stamped, bus will meet you on the other side.  Take the bus to end of line, which in the bus station in Argentina.  Note: This bus parks in the second stall.  go to other end of the terminal to the last booth called Catararas Waterfall and buy round trip ticket to falls for 7R, take the bus right in front of it to end of line (comes every 20 min), which is the Argentina Falls.  Note where bus stops at Falls, so you know where to go back to for the return.  To return, repeat steps backward.  However, after Argentina passport stamping, the bus will take you to the Brazil passport station.  You will have to get out there and get your pasport stamped.  The bus does not wait for you this time.  Instead, you need to go to the bus stop right there and take the next bus that goes to "Centro"  (the bus to Brazil border is $R4 and then bus to Centro is $2.65).

Important note: The park entrance on the Argentinian side of the falls only accepts cash payments in Argentinian pesos. They do not accept credit cards or debit cards, nor do they accept Brazilian reais (or U.S. dollars or any other currency). And there is no ATM at the park entrance (suppouselly there should be one, but the oficer there may change the currency for you at his exchange rate). In other words, make sure you bring enough pesos to get into the park (130 pesos as of June 2012). You will need to either exchange some money before you go into Argentina or you will need to find an ATM once you are in Argentina. There is a bank about a block away from the bus station in Argentina where one can withdraw pesos using an ATM card.

It is recommend that you bring enough Argentinian currency to pay the entrance fee to be safe.

It is recommended to see Brazil side first then Argentina side because the brazil side is gorgeous, but the Argentina side is the Grand Finale.  Also note the boat rides didn't seem as great as the hype the guides books say.  For 28R you get absolutely soaked, so if wet underwear is your thing, then you should go.  However, you can get the same close up pictures from the Argentina side on land.