Read. It’s as simple as that. Talking books is the way to her heart. And, if you really enjoy a book, you can recommend it to her which equals mega brownie points— that is, if she enjoys it too.
Converse. Even if they seem quiet at first, girls that read have plenty to say. Just make sure you do too. The last thing you want is to bore her. She’s accustomed to being engaged, so don’t disappoint her.
Be yourself. Readers are curious and love to learn. Talk to her about your hobbies and interests; it doesn’t matter if they’re book-related.
Ask questions. Figure out what genres she likes to read, what her favorite authors are, and what she’s reading ATM.
Understand that, at the end of the day, she is so much more than an avid reader. Maybe she’s also an amazing athlete or actress. Regardless, she’s a human being, so treat her like one. Get to know her, and appreciate what makes her the fascinating girl that she is. Because, trust me, she is fascinating. We all are, just in different ways.