Pretty much everything we see in this novel is from Ella's point of view, because she is the "I" narrating events as they happen to her. This helps us sympathize with what would otherwise be some very strange behavior, such as when she follows commands that don't serve her best interests. Every time Ella's commanded to perform some odious task—giving her mother's necklace to Hattie, or scrubbing the manor's floors with lye according to Dame Olga's orders—we sympathize with Ella since we see things through her eyes.
It's not all straight-up first person, though. When Ella tells us about being cursed at birth, it's pretty obvious that she wasn't able to narrate the event, having just been born and all. But the people who were there—her mother and Mandy—have clearly told Ella exactly how it went down:
I could picture the argument: Mandy's freckles standing out sharper than usual, her frizzy gray hair in disarray, and her double chin shaking with anger; Mother still and intense, her brown curls damp from labor, the laughter gone from her eyes. I couldn't imagine Lucinda. I didn't know what she looked like. (1.3-4)
The other people in her life help Ella patch together her early memories, so that she's conveniently able to narrate them in the novel for us, even if she doesn't remember them as sharply as people who were adults at the time did. Ella says of her curse: "My first awareness of it came on my fifth birthday. I seem to remember that day perfectly, perhaps because Mandy told the tale so often" (1.6). Because we all love to tell embarrassing stories about kids, right?
In addition to other people's stories, there's one other perspective trick that lets Ella (and us) see more than what her first-person perspective will show her. The fairy-made book that Mandy gives Ella will show her images of other people, their letters, and even their journal entries. Apart from the fact that this is mildly (or majorly) voyeuristic and also possibly a little unethical, it shows Ella what those around her are thinking, feeling, and planning so she can react appropriately.
And hey, when you're under an obedience curse, you have to use every tool at your disposal, no matter how shady.