From Rio de Janeiro there are frequent buses to Angra dos Reis on a trip that takes approximately 3 hours. You can also get to Angra dos Reis from Paraty on a bus trip that lasts 2 hours.
From Angra dos Reis there are several boat services that reach Ilha Grande.
There are catamarans and more tourist boats and other cheaper and slower services that serve as public transport for the people who live on the island.
See more about the location of Ilha Grande
See also information on Angra dos Reis y Paraty.