Need help configuring new user signup email notification
The workflow for registering users can be configured at index.php?q=admin/user/settings. If this does not suit your needs, let us know how your workflow differs from what can be configured on that page.

I suspect you want to check the option Visitors can create accounts and no administrator approval is required. and uncheck the option Require e-mail verification when a visitor creates an account. The e-mail that are sent can be configured in the fieldset User e-mail settings and for some e-mails, you can configure whether to send them at all.