I suppose it’s something I’ve not addressed particularly clearly in the examples either online or in the blogs I’ve written so far. Essentially the form value is going to be available from a React context consumer that you can import.
This consumer is used by the FormButton component (available in the associated Atlaskit renderer package) for example and passed to the onClick handler. The form value itself is available in the onChange handler for the Form component (for example in cases where you might want to submit on valid form changes).
You’re right that I should do a better job in providing more concrete real world examples.