The important part for answering this question is: In the second book of the series (New Moon), he discovers that he can shapeshift into a wolf.
This justifies what answer for what question? Q & A:
Passage: Jacob "Jake" Black is a character in the Twilight series by Stephenie Meyer. He is described as an attractive Native American of the Quileute tribe in La Push, near Forks, Washington. In the second book of the series (New Moon), he discovers that he can shapeshift into a wolf. For the majority of the series, Jacob competes with Edward Cullen for Bella Swan's love. In the films Twilight, New Moon, Eclipse, Breaking Dawn: Part 1, and Breaking Dawn: Part 2, Jacob is played by Taylor Lautner.

Question: Based on this passage, when does jacob find out he's a werewolf?
In the second book of the series ( New Moon )