The main settlement on the island is called Vila do Abraão and most transport goes to there. There are three main ports on the mainland from where boats regularly leave for Abraão: Mangaratiba (closest to Rio), Concecao de Jacarai (the one closest to the island and with most connections) and Angra dos Reis (closest to Sao Paulo). There are slow boats with capacity of 500-1000 passengers that cost 15
reais (prices in this paragraph as per Feb 2016) and they usually leave once a day from Mangaratiba and Angra. There are also more frequent fast boats for 15-30 people that cost around 30 reais (to Jacarei) and there are taxi boats that cost more. [http://www.ilhagrande.com.br/como-chegar/horarios-para-abraao/ This website] has some timetables (all in Portuguese but easy to understand with google translate).
To get from Rio to Mangaratiba/Jacarei/Angra you can take the Costa Verde buses from Rodoviaria in Rio. It costs 54
reais to Jacarei/Angra. You can also get there by changing three or four public buses for less than 20 reais but you need to figure out the connections (basically from Itaguai there is a public bus for 3.60 reais that goes to Jacarai).
There are also some tour companies that sell a door-to-island package for a van and boat. These cost 95+
reais one way and they pick up from locations in the touristic parts of Rio.
To get to Ilha Grande you have to take a boat.
Ferries operated by Barcas SA [ 1] Mangaratiba (105 minutes, starting 8:00 a .m., return 5:30 prices are much more expensive than those charged by Barcas SA , which is the government. The Barcas SA are of the government of Rio de Janeiro is much safer and their staff are top professionals. Terminal Santa Luzia is discouraged . Their prices are much higher than Those of Barcas SA . Another problem is the operating company of this pier, it offers a fast boat, but at the time of shipment you can embark on a slow boat extremamante. Their employees are rude and unprepared to deal with tourism.
Best way to get to the island from Rio is to take the 05:00 Costa Verde bus to [[Mangaratiba ]] (R$ 30. 5 as Sep-14), it will leave you at the dock a little past 07:00 so you'll have time to have breakfast and take the 08:00 Barca to Ilha Grande (R$ 14). You can buy the tickets for the Barca right there in a booth, it won't be full because it has a 1000 passengers capacity.
If you come from the city of Rio de Janeiro to [[Angra dos Reis]] and landed at the Bus Terminal, you can take a taxi or walk to the port of Angra dos Reis, is very close and relatively safe.
Another option to get on the Ilha Grande is to go to Conceição de Jacareí which is a district of Mangaratiba or in the center of Magaratiba (address: Rua XI Novembro without No. Mangaratiba) preferably at using Barcas SA, which also operate these terminals . Avoid illegal vessels in Conceição de Jacareí are extremamante dangerous and uncomfortable. The Barcas Sa also operates the route between the Conceição de Jacareí to Vila do Abraão in Ilha Grande. (Being more comfortable and organized in Angra dos Reis to the Vila do Abraão).
Important to note is that there are no banks on the island, the money should be brought since not all hotels, shops and restaurants accept credit cards. From Rio de Janeiro, you can now book online for door to island transfers with the Green Toad Bus [http://www.greentoadbus.com/en/Brazil-bus-passes/Transfers-ilha-grande-307] website. Pick-up from your hostel then a 3 hours drive to the docks where the transfer to a boat to travel 30 minutes to the island. You stop at an ATM cash-up before hitting the island which has no ATM machine. They also have bus trips starting from Sao Paulo and Paraty. Daily buses operated by the Costa Verde  out of Rio de Janeiro to Angra dos Reis and Mangaratiba. Daily buses from São Paulo to Angra dos Reis are operated by Reunidas Paulista . Who comes from Rio de Janeiro City, unfortunately, have to use the bus company Costa Verde, with officials unprepared to deal with tourism