Customer accounts are available in the Web Store and Inquiry Catalog modes. To automatically create the customer account on the first order, set Remember fields by to User Account. This option is located in Products > Settings > General Settings > Shopping Cart (Quote Cart in the Inquiry Catalog mode), in the Form Settings section. The default Cookie Save option only remembers the form fields in the visitor’s browser.
After that, make sure that your User Email template in the same settings screen has the [account_info] shortcode included (it is in the default template). It prints the login and password for the new account inside the order confirmation email. See Checkout email notification shortcodes.
Now each time a new customer orders something an account will be created.
All the checkout info will be saved so the customer doesn’t have to fill all the information again.
If you also want to let the customer see the order history, set up the customer panel.