In Terminator 2: Judgement Day, Sarah starts off being terrified of the Terminator.
Then she accepts its presence, primarily because it is useful to her at the time, but she still doesn't want it around.
In a deleted scene, the Terminator reveals that its CPU is set to a "read only" setting, and if they want it to learn how to behave like a human, they need to open its head, pull out the CPU chip, flip a switch, and reinsert it. After Sarah has pulled out the chip, which also has the effect of shutting down the Terminator, she attempts to smash it, but John stops her, pointing out that they need the Terminator's help if they are going to live long enough to stop Skynet. She reluctantly accepts his argument, and allows him to reinstall the CPU and reboot the Terminator.
She gradually becomes more tolerant of the Terminator, but still remains aloof from it, and doesn't interact with it very much. Still, in the scene in which they are at Enrique's camp, her narration says that she now knows that the Terminator is the best possible guardian for John, and is not susceptible to the same flaws that human men are - "It will never get angry and hit him, it will never be too busy to spend time with him", etc.
Finally, at the end of the film, just before she lowers the Terminator into the molten steel, she smiles and shakes his hand, showing her respect for him and everything he has done for her and John. In her outro narration, she even goes so far as to say that the Terminator taught her to appreciate the value of humanity.
Is there any explanation of when she began to trust the Terminator? If such information is available, I imagine it would be in the novelization.