The Late Registration extension allows customers to skip the registration process at the beginning of the checkout, and presents the option to complete registration once they have placed their order. This feature speeds up the checkout process for customers, while still allowing them to register for your site, and receive the benefits that may come with being a registered customer.
Once you have the Late Registration extension installed, the setup for enabling will appear as per below in the backend (via System > Configuration):
You also have the option to "Hide Method Options". If this is set to "Yes" then you will not be able to select 'Checkout as Guest' or 'Register and Checkout'. You will be directed straight to the checkout, and be able to fill out shipping and payment information. If you set "Hide Method Options" to "No" you will be able to select 'Checkout as Guest', however the ability to register will now be available after you have placed your order.
After filling out all the required information and placing your order, you will be redirected to an 'Order Success' page. Also on this page will be the option to now register for an account (with all the information entered at checkout), you need to insert a password in the required space, and then click 'Register for an Account'.