When interacting with web pages and other documents using Orca, you are interacting with the document itself; not a buffered copy of that document. Thus there is no special mode to get into or out of when you wish to fill out a form. Instead, simply navigate to each field whose contents you wish to change, and interact with the widget as if it were in a dialog box.
To navigate amongst form fields, you have several options:
Use Tab and Shift+Tab, to navigate amongst focusable objects, regardless of type.
Use Orca's structural navigation commands for forms.
Depending on the form, you may also be able to use Orca's caret navigation commands, in other words, the arrow keys when Orca is controlling the caret.
Because there is no special mode in Orca for interacting with forms, the most frequently-asked question is how to exit a focused form field. For this, too, you have several options:
Use Tab/Shift+Tab if you wish to leave the currenty-focused form field and move to the next/previous focusable object, regardless of what that object happens to be.
Use Orca's structural navigation to move to the next/previous form field: Orca Modifier+Tab/Orca Modifier+Shift+Tab.
Use Orca's commands for moving to the next/previous object or chunk of text: Orca Modifier+Right/Orca Modifier+Left.
If you are not in a list or combo box, you can use caret navigation commands to arrow out of the form field, as long as Orca is controlling the caret.