Tokien indicates that Thorin is the leader in both superficial and more complicated ways. When Bilbo first meets the dwarves, Thorin wears a light blue hood with a silver tassle, as well as an expensive golden belt. He asks for wine, whereas all the other dwarves ask for tea and beer. Thus, right from the beginning, Thorin asserts his status as the rightful king under the mountain.
But Thorin's authority goes beyond his appearance and his beverage preferences. He is unflinching in his belief that the treasure under the mountain belongs only to him and his kin, and the other dwarves do not deny this, even though some of them might be uncomfortable with his assertions. From their encounters with the woodelves to the men of Dale, Thorin's only concern is for his companions. At times, this loyalty is foolish, but Thorin does not sway until the end of the book, right before he dies.
Still, Tolkien makes it clear that Bilbo is the true leader of the company, as even Thorin begins to rely on him. Once they enter the forest of Mirkwood, and lose Gandalf's guidance, it is Bilbo's wit and cleverness that gets them out of multiple scrapes. Thus, Thorin might be making the ostensible decisions, but he really is only a figurehead.