The short answer to your question is that Drupal gets its power comes from bringing many different toolsets together. The user registration form is made up of functionalities from many different parts of Drupal's APIs. There is no one place to go to change the working of this form. You can get better help if you ask a number of more specific and focused questions.
You seem to have at least 5 different problems (as elaborated in your comments).
You need a field, as @JamesShields said. This can either be a custom field from your custom module, or from the Address module. Installation process for Address requires composer, an is discussed here: https://bojanz.wordpress.com/2015/09/18/d8-composer-definitive-intro/
FIELDS: You need to add the field to the user account settings, as @Shabir said, at admin/config/people/accounts/fields
EMAIL: You need to do something to do with emails, either
a) modifying the built in emails at admin/config/people/accounts,
b) waiting until March when the Rules module hopes to become usable, or
c) sending emails from custom code in response to the user registration.
I could not find a code example to help with c), you may have to start a new question for that.
REFORMAT: to reformat the form, you need to find the right twig template. Turning on twig debugging is a good place to start with this. See http://www.zyxware.com/articles/4531/drupal-how-do-i-turn-on-twig-debug-mode-in-drupal-8
VALIDATE: If you require validation beyond what is supported by the available fields already, then you want either the entity validation API or the Form API, from custom code. The examples module is a good reference, or a more basic tutorial from Google.