Documenting the design process of a GUI involves recording and sharing information throughout the design journey. Here's a suggested approach:

1. Design brief: Outline project goals, objectives, and requirements.

2. Research and analysis: Document user research, personas, user journeys, and competitor analysis.

3. Wireframes and mockups: Create and share low-fidelity sketches and high-fidelity prototypes.

4. Design specifications: Write detailed design specs, including layout, typography, color schemes, and imagery.

5. Style guides: Develop and maintain a living style guide for consistency.

6. Design decisions: Record rationales behind design choices.

7. Prototyping and testing: Document testing plans, results, and iterations.

8. Iteration history: Keep a record of design changes and iterations.

9. Design system documentation: Document reusable components, patterns, and guidelines.

10. Final design files: Share final design files, assets, and specifications.

Tools for documentation include:

- Design documentation software (e.g., Notion, Confluence)

- Version control systems (e.g., Git, SVN)

- Project management tools (e.g., Asana, Trello)

- Design collaboration platforms (e.g., Figma, Sketch)

- Word processing and spreadsheet software (e.g., Google Docs, Microsoft Office)

Remember to tailor documentation to your project's specific needs and audience.