Shortly after she is revealed on Kobol - and after he assaults her, resulting in her saying, "And you ask why?" which is an answer to the question he asked the corpse of Boomer back on the Galactica - Caprica-Eight is confronted by Meier, one of Tom Zarek's men, who tells her that not only was Boomer murdered by Cally, but that Cally then only received 30 days in the brig for unauthorized shooting of a gun. Caprica-Eight is obviously concerned with this - "Cylons aren't people." - and asks Helo to "trust her, trust us," because she has to take matters into her own hands.
As a back story for those of you who either don't remember this episode or have never watched the show, Tom Zarek and Meier were planning on killing Lee in some way so they could get some leverage with Roslin. Once Adama shows up on Kobol, however, their plans are shot to hell, at least in Zarek's eyes. They seem to have wanted to use Caprica-Eight as a tool, anyway, probably thinking that she was simply just another version of Boomer, but Caprica-Eight sees right through this ruse, particularly after Meier decides that he will complete his mission, regardless of Zarek's approval.
Anyway, as they approach the Tomb of Athena, Caprica-Eight colludes with Meier, telling him to handle the son while she takes on the father. The rest of the group arrives, and Caprica-Eight aims her gun right at Adama's chest, a la Boomer, while Meier proceeds to hold Lee at gunpoint. Of course, Caprica-Eight then shoots Meier, only to return her aim at Adama, saying,
"I'm Sharon, but I'm a different Sharon. I know who I am. I don't have hidden protocols or programs lying in wait to be activated. I make my own choices. I make my own decisions, and I need you to know this is my choice."She allows Adama to take the gun from her, and Meier confesses to a saddened Zarek that he was just trying to make sure that Zarek got what was due him.
This very moment marks the beginning of Adama and Athena's friendship. She spends much of her time over the rest of the season proving that she is an ally to the humans, actions that are ignored by quite a few people. It isn't until well into the third season that she's accepted as a member of the Fleet, even after she's commissioned as an officer to assist in the rescue on New Caprica. Cally accuses Caprica-Eight of planting a bomb on a Raptor, which was actually the work of a fellow human trying to kill Romo Lampkin, Baltar's lawyer during his trial for treason. Adama places her in the brig again after she shoots Natalie, a Number Six model, an action driven by a vision she had that showed a Number Six taking her daughter away from her. But eventually, Caprica-Eight is viewed as trustworthy and also, more importantly, a member of humanity, not just a "thing."