Answer:
The answer to this question is not found on any single page in The Lightning Thief.
Percy discovers his water powers during his quest to retrieve Zeus's lightning bolt, which is spread out across multiple chapters in the book.
He first discovers his power to control water when he saves Grover from a group of bullies in Chapter 7, and he further develops his water powers in Chapter 12 when he saves himself from drowning in the River Styx.