To get from Buzios to Ilha Grande on shared transport it is necessary to travel from Buzios to the Rio international airport on a regular transfer first, before changing to another service to Ilha Grande. On the second leg of the journey, you will be taken to the coastal town of Conceicao do Jacarei and then swap to a passenger boat which will take you to the main town on Ilha Grande called Abraao. Once on the island, you make your own way to your accommodation, because there are no vehicles on the island to take you there. We would suggest booking a hotel in Abraao which offers easy access by walking.
A faster trip would be to reserve a private transport between Buzios and Ilha Grande and have a driver take you directly to Conceicao do Jacarei, where you will be provided passage on the next boat departing for the island.