Today I have just completed a successful one day return trip using public transport to get to Iguazú Falls in Argentina from my hostel in Foz do Iguaçu in Brazil. It was a cheaper alternative to using a private hostel package and really was not as complex as people make it out to be. The journey does take around two hours each way so if you are short on time for whatever reason, i.e. nursing a nasty hangover then perhaps get a private car for convenience. However, we left the hostel later than planned (around 9:30am) and still had more than enough time at the falls.
Important: You will need to bring your passport
Step 1 - Getting the Bus: At the bus station in Foz do Iguazu town Brazil (Terminal Touristic Urban or TTU) there is a bus stop which has a faded, small white sign which details Iguazu Falls Argentina. Ask your hostel for directions or a map if you don’t know the station. The stop is positioned at the front of the platforms closest to the zoo, if you are facing the zoo it will be the platforms on the far right. I believe that the buses depart every 40 minutes and they currently cost 3.50 real per person at the time of writing.
Step 2 – Get your voucher: Once you have boarded the bus you should be handed a paper ticket or voucher that will enable you to board another bus for free after you have been dropped off at Brazilian immigration. The first bus will not wait and you don't want to waste money by paying again for the next one. If the driver doesn't give you a ticket when paying remind him that you will need you passport stamped at immigration and need a voucher.
Step 3 – Brazilian Immigration: After the driver drops you off at Brazilian immigration and you get your exit stamp from Brazil in your passport there is a bus stop just past the checkpoints on the right hand side. Use your ticket to board the next bus for free although you may have to wait a while depending on the frequency of the company buses. If the bus of an alternate company goes through you could always pay again to save time.
I made enquiries as to whether it is possible to simply walk to the Argentine border. It's possible in theory but as it is over 1.5 kilometres and dangerous according to a customs worker, it's not recommended. I assume the danger relates to the cars as there are no pavements (or sidewalks to our yank friends).
Step 4 – Argentine Immigration: On your second bus you will need to get off along with everyone else at Argentinian immigration in order to get the entry stamp for Argentina, but don't worry this time the bus waits for you provided you don't spend ages changing currency or anything silly.
Step 5 - The bus station: Now you are in Argentina, the bus you are on will drive you to Puerto Iguazu bus station where you will need to get a new bus to get to the actual falls. Tickets are sold at the office of a company called 'Practico S.R.I' and their buses depart every 20 mins costing 7.50 pesos per person at time of writing (you can pay equivalent in real). It is a good idea to buy a return ticket at the office whilst you are there. The bus will drop you right at the park entrance for your wonderful waterfall experience and all at a fraction of the cost of a private car.
To get home repeat the journey the other way round but pay attention on the first bus back to Puerto Iguazu bus station as our bus didn't actually pull into the station and we had to get off just before. Your bus driver should announce this like he did with us but it was far from clear what he meant.
I hope this helps, good luck and have a great time. Please comment if need be.