What does your strategy-planning process look like?

First we build a roadmap for applications/services needed in the next 1-5 years, for that we meet with all the areas from bottom-up. Once we have the needs we connect the dots and establish a dependency map and all investments needed (time, labor and other resources).
That roadmap is presented to top management to have their input and approval for next year, with revisions each semester.

My strategy process planning involves these steps:

1. Becoming familiar with the business landscape. I review the mission statement, business objectives, short term goals, midterm goals, and the 5-year goals of the organization. 
2. I meet with the section heads to learn about the issues that are affecting them and the business.
3. I identify some low hanging fruits and address those issues to build an immediate credibility so the functional areas would trust IT and partner with IT in major business transformation efforts.
4. I take an inventory of workflows, manual processes, automated processes, ad-hoc processes, and reusable processes.  I often engage a business analyst and/or an Enterprise Architect who's certified in TOGAF in this stage. We use the TOGAF model, Porter's Model of Competitive Forces, and SWOT analysis in this phase which I often label as the study of "Current Operating Mode."
5. We compile a list of 16 projects for our 3-year technology roadmap.
6. We prioritize 5 projects from the list above that have the highest financial impact or risk mitigation to the organization.
7. I create business proposals by using the SDLC framework to show the benefits of these projects or threats involved if the organizations chooses the "Do Nothing" option. TCO, ROI, Cost-Benefit's Analysis, and NPV are often quoted here.
8. I secure the organizational buy-in by partnering with the Executives and Section Heads. One has to cultivate an "atmosphere of trust and collaboration" to achieve this goal.
9. I present the 5 major IT initiatives to the Executives, and if needed to the Board.
10. I create project plans (or have my project manager do that) for these projects once they get approved.

On would never fail on the execution of IT projects and the delivery of technology solutions when the Executive Commitment and support is in place.

I reckon that prior to thinking about who to engage and the mode of engagement which is already well covered by many in this forum, I would focus on the thought before that.

Specifically, prior to initiating any fact finding or communication for strategy-planning, it is important to always start with an end in mind. What is the focused objective we are planning to achieved, or what are the challenges that we are trying to achieve?

In today's highly competitive and unceasingly fluid landscapes, it is an art to balance between "innovate or evaporate" and "strategizing a solution looking for the problem". At one end of the spectrum, we need to continuously strategize and innovate as no one would like to be in the position to wake up a day and say "who moves my cheese?". At the other end of the spectrum, we truly do not want to drive strategies or innovation and channelling resources into creating technology rainbows.

The starting thought can be a critical success or failure factor of the entire strategy-planning process. Ask ourselves the above mentioned questions before we even initiate the journey and start engaging people. In Singapore, success stories all of us know well have nothing to do with advnaced technologies. Some of which are the car parking apps and the trace together app.

So let's start with a practical end in mind. The way we engage and fact finding that come next is a large subject that depends very much on the company structure and culture, and it would vary substantially from organization to organiziation in my view.

To start the strategic planning exercise on the right foot, I bring together the right participants. Among the stakeholders, creative people and people who have a good understanding of the operations. Of course, i bring leaders and the head of the company to participate and support the process in order to maximize the chances of success. That said, it's not just about getting the leaders together, the involvement of key employees is important too. Among those who will take part in the exercise, designate the people who will be in charge to keep track of the activities and consolidate everything.
I am often accompanied by an external consultant for your strategic planning. Someone with experience and more neutrality can make it easier for you, get you out of your comfort zone, and help the process go smoothly.

For us its two parallel tracks that merge into one. In one track there is a lot of interviews with stakeholders to map out the commercial needs that the technology teams needs to support, and in the other track we look at the more technical areas (Infrastruckture, SecOpe, Biz Apps, etc) and map out what platform lifts and changes we need to strive towards so we maintain secure, stable and supported systems. These two tracks then eventually merge into one strategic picture which makes up the IT Strategy.