You need to add the new fields to the model, and then to the form. The non-technical solution (without writing a module yourself) is:

1. In Settings, go to Technical -> Database Structure, find the model to change and edit it, then add the fields extra you need.
2. In Settings, go to Technical -> User Interface, find the form and edit it's Architecture text. Look for tags <field> to choose a place to insert your new fields. A field can be added to a form by inserting a line such as <field name="my_field_name"/> next to other field tags.

You can find more details in this answer.