By bus
It is very easy to get to Blumenau by bus. There are several interstate companies with regular lines to Blumenau and region. A trip from São Paulo takes about 10 hours and costs about R$100,00 (US$45,00) one-way. The bus station is open 24 hours a day and has showers free bathrooms and a diner (however those are very old right now and very dirty, and only snacks are available and the bus station whose is very dangerous indeed). It is served by urban buses to PROEB (downtown) and Fortaleza (neighborhood) Terminals. There are also taxis, which would take you downtown for about R$15,00 (US$8,50).
By plane
The nearest airport is Ministro Victor Konder International Airport, located 59 km away in Navegantes, with flights only from Sao Paulo and Porto Alegre. In the airport there buses to take you downtown Blumenau. GOL Linhas Aéreas also has free buses for its costumers.
It may be easier to find airplanes to Santa Catarina through the Aeroporto Internacional Hercílio Luz, in Florianópolis, but from there you must take a bus or a taxi to Florianópolis Bus Station and from there, a bus to Blumenau.
Or also take a flight to Curitiba airport (located in the city of São José dos Pinhais) and take a bus from Catarinense Viação Bus company directly without having to go to Curitiba central bus station. You can go to the Bus point called 'Pinherão' located in the center of São José dos Pinhais with is located about 30 min. by foot or 10 Reais by taxi.
By car
If you are not far away, you can come by car. The main road in the coast of the State is BR-101, but there is no way to get into Blumenau directly through this road. You will have to use either BR-470 (which is very dangerous),or SC-470, known as Rodovia Governador Jorge Lacerda, which goes through the cities of Itajaí, Ilhota and Gaspar. This road is not as fast as BR-470, but it's much safer, has less trucks and it is better