First go to your cart and make sure you do have all the products you want to purchase. Remove and/or add any products to adjust your cart as you please. Then click on the 'Pay' button. There is one large pay-button at the bottom of the shopping cart and one smaller one at the top right of the webpage.
If you do have a product in the cart that needs to be mailed the next page will allow you to select shipping options. In most cases you will have only download products. You will then immediately get to the payment page. On the payment page you first need to select how you would like to pay.
For most this will either be with Paypal or Credit Card, therefore select the 'Paypal, Credit Card' option. This will expand the selection and you will see a choice for Credit Cards and another choice for Paypal. (Make sure Javascript has been enabled. If Javascript is not turned on this expansion does not happen.) Click on which one you would like to use.
If you choose Paypal you will see a yellow Paypal button appear. Click this yellow Paypal button and you will get to the login for your Paypal account.
Once you return from Paypal and are back at the Lybrary.com website continue your checkout to the end until you have confirmed your order.