the linha turismo bus operating in curitiba is fantastic. for $10Real you get a days worth of travel on a bus around the key tourist sites in curitiba - 22 to be exact. it is a two hour round trip. your ticket allows you to get on and off 3 times so make sure you decide which are your must see destinations first.
as a bonus they have a recording on the bus in english, portuguese and spanish to let you know exactly where you are and why it is important.
the train ride between curitiba and paranagua is not to be missed. the gorgeous descent goes through rainforest and 13 tunnels and cross more than 60 bridges. the view is magnificent. the ride takes about 4 hours one way. the best view is if you sit on the left hand side on the way down. buy tickets on the day you want go from the train station.
International airport, 20 minutes south of the city centre. There's a public bus going there, but not very often, unfortunately you must rely on taxi. International flights are not so common, but there are lots of daily connections with Sao Paulo, Rio de Janeiro, Foz de Iguaçu, Florianopolis.
Bus transport is very efficient: arrival/departures from the 'Rodoviaria', 10 minutes walk from the city centre. Buses are going to almost everywhere in Southern Brazil, frequent connections to Sao Paulo (6 hours), twice a day direct to Rio de Janeiro (12 hours). If you want to travel at specific schedules, it's advisable to book in advance.
Rail: ... as usual in America, they are almost useless. It's worth knowing that a special (mainly touristic) train runs daily from Curitiba down through the Sierra do Mar to Paranagua. It has a very scenic route, with very nice views of the Atlantic rainforest and through the mountain rage dividing Curitiba from the Atlantic ocean. The railway itself crosses spectacular spots. If you want to travel on week-ends, you are requested to book in advance, especially during summer (December to March).
Well, Curitiba is world-know for its extremely efficient public transportation system. Try it! And don't miss the 'Ligeirinho', the grey-painted express lines, which alows you to cross the town in a matter of minutes.
A nice network of cycle-ways allows you to safely ride through the city traffic and to reach the most important leisure spots, such as parks, theatres, halls.
Curitiba has probably the best planned public transport system of all Brazil, if not of all major cities in South America. Take advantage and see the city on a bus