You enter the VAT number when you are at the final purchasing stage of the process.
If you go to Leanpub, look in the top right corner. There is a shopping cart icon there. If you click on it, you will see any items that are currently in your shopping cart. If you see no items there, you need to add the book to your shopping cart again.
Once a book is in your shopping cart, go to the shopping cart by clicking on the icon, and then click the blue "Continue to Checkout" button.
After you select a VAT country, you will see the box to add a VAT number in our credit card form.
The process will be similar if you are using the PayPal checkout option, instead of our credit card form.
(If you would like to check the validity of your VAT number, please go here: http://help.leanpub.com/reader-help/your-purchase-form-is-rejecting-my-vat-number-what-can-i-do.)