Q: How do I transfer a book on iPad to my iPhone?

There isn't a way to directly transfer, you can either copy it to your computer's iTunes (via File > Transfer Purchases) and then sync it to the iPhone, or you can re-download it directly on the phone via the Purchased tab in the store : re-downloading.

For future purchases you can also turn on 'automatic downloads' for apps, music and/or books (though that will use some of your data allowance if you aren't on wifi) : http://support.apple.com/kb/HT4539