How can I go about helping someone else organize for better personal productivity when they have recognized a need to do so?
Clarify your role: First, I'd probably step back and look at the relationship, are you the person's colleague? Family member? Supervisors? Subordinate? According to different power structure the ways can be quite different. But generally this is how I'd approach it:
Identify the domain(s) to be organized: I'd first have a talk with the person and have him/her identify the incidents that prompted him/her to want to get more organized. Get as many details as possible. For instance "I overbooked twice this week." "I missed deadline on three projects last months." "I can never make even 30 minutes to be with my children." etc. This stage is crucial because you need to craft an achievable goal with him/her, and these problems provide the foundation. This is also a good stage to figure out if the goal would be too ambitious, e.g. "I want to clear up all my projects in hand so that I can go to honeymoon next month without any worry."
Gauge his/her commitment and urgency: Gently size up the potential gain/loss if the person gets or does not get more organized. If it's an ultimatum from the big boss, then you can consider some more extreme methods; if it's just usual little whining, then you may want to dial down the difficulty.
Examine his/her adaptation style: You'd need to try your best to discern how the person learns best. Some people can pick up the system just by looking at other people following it. Some may need a book, some may need a blog, some may want an infographics, and some may need to constantly communicate with others to ensure the procedure was right, while others may work well enough just with a letter-size reminder taped on the wall.
Introduce appropriate materials and methods: Depend on what you found above, plan a program for the person.
Tracking successes and areas of improvement: After a certain period of time, revisit the root problems and assess if the intervention is successful. Share what worked or not, and modify. If there is another goal, repeat the process to address the new problem.
Some other strayed thoughts:
I would offer to show my personal productivity system to the person. From there, I would discuss the points that she liked and disliked about it.
Based on the person's feedback, I would offer to start helping or coaching.