If the Smart Transaction is prepared for checkout, you can access the checkout URL in the field /checkout_links/url_checkout:
It is up to the merchant to offer this URL to the prospective customer.
A few suggestions:
It can be opened full screen in a browser using an <a> tag.
It can be opened in a modal layer that is able to show an arbitrary HTTP source.
It can be sent via e-mail or in a chat window to a known customer.
When you integrate it into a web application you should define return URLs. There is a section below, that describes how to define them. But as you see it is not bound to a website or web application.
When you open the Checkout Wizard in a layer, you need to consider that it might switch to full screen mode. This is needed for instance for the 3-D Secure checks.
The return URLs will always open in full screen and replace the former window.