How to transfer Kindle Book

I just bought my first Kindle Book today from Amazon and it was downloaded automatically to my Z10. It looks great and everything but I really would prefer to read it on my Playbook with the larger screen. I do have a Reader program on my Playbook.

How can I transfer this book to my Playbook? Also, can I have the book on both the Z10 and Playbook?

Thanks for any help.

Paul