How to enable guest checkout in PrestaShop
By default, PrestaShop is configured so that only registered customers who have an account on your site can order products. Visitors cannot order without creating an account. If you want to, however, you can enable guest checkout. There's an option in the admin panel with which you can do that.
If you use PrestaShop 1.5 or a newer version like PrestaShop 1.6, log into the admin panel, go to Preferences menu>Orders sub-menu, set the option Enable guest checkout to Yes and click on the Save button.
In PrestaShop versions older than 1.5 (e.g. PrestaShop 1.4) after you log into the back office click on the Preferences menu, on the page that opens set the option Enable guest checkout to Yes and click on the Save button.
When guest checkout is enabled some options will be added to the Login step of the checkout process. Unregistered customers can use them to specify their personal information (e.g. name, email address, etc.) and provide a delivery/invoice address. Once the order is placed PrestaShop will automatically send them an email with the order details and ID.