Schettino is accused of multiple manslaughter, abandoning ship and causing environmental damage over the Costa Concordia disaster off the island of Giglio.
"We're here today to get justice," Francesco Di Ciollo, who represents two Italian families, said ahead of the start of the hearing in Grosseto,the city nearest to the crash site.
"Survivors have to live with anxiety for the rest of their lives. There was darkness, panic, they were stranded inside without a way out," he said.
"We're expecting it to last more than a year," said Massimiliano Gabrielli, a lawyer for some of the survivors.
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The Costa Concordia crashed off Giglio on the night of January 13, 2012 with 4,229 people from 70 countries on board, killing 32 people.
Schettino was nicknamed "Captain Coward" for leaving while terrified people were trapped aboard the cruise lliner and then sobbing in the arms of the ship's chaplain.
The 52-year-old has been depicted as a blackguard who was showing off for a blonde female guest when he performed a risky manoeuvre to "salute" the island.
Gabrielli, part of a group called "Justice for the Concordia", accused Costa of "choosing to save the ship instead of saving people", a reference to the delay of over an hour between the crash and the order to abandon ship.
Gabrielli also said Costa had scored "an own-goal" by accepting limited responsibility as Schettino's employer before the start of the trial and agreeing to pay a fine, pointing out this could open the way for further legal action against Costa.
They plan to probe Costa Crociere management, materials used to build the ship, and the apparent malfunction of emergency doors and back-up generators.
"He did not abandon ship," said Donato Laino, another lawyer for Schettino.
"If he had stayed another 10 minutes he would have fallen in the water and not been able to manage the evacuation.