Interesting question. Start by developing an understanding the science of diversity and inclusion. Understand the equation where a more diverse and broad talent pool and an inclusive culture/business practices leads to better creativity and innovation, which then results in new products, that then open up new markets, that then generates a superior financial performance. (This is one standard D&I to Innovation to Competitive Advantage to Profit equation).
Truly, do the utmost to learn the science of innovation through diversity and inclusion. Build a case with quantitative examples to demonstrate D&I's linkage to Innovation, and its tangible, value in commercial operations (to convince your financial nay-sayers, try using a visual Dupont Analysis).
Then turn your attention to the basic work unit - the team level - starting with the training of senior leaders of teams. Begin with an analysis of each leader's work style using the Pioneers, Integrators, Drivers, and Guardians work style model. If you are like most firms, you will discover that Pioneers and Drivers are dominant, and that by nature and habit (and in the absence of training to build inclusion competencies), they overshadow Integrators and Guardians. You will find, if you run surveys or focus groups of their direct reports, that most leaders are by nature, not inclusive and more often than not, an impediment to innovation. Once Pioneers and Drivers are made aware of how they overshadow and stress out Integrators and Guardians, and how some of their direct reports feel excluded and refuse to speak up in brainstorming / creativity sessions, they will be more open to learning how to better foster innovation. I have found that two or three sessions on work styles along with experiential learning exercises, does the trick. Depending on leadership's responsiveness to this topic, you may also use the results of a work culture assessment, and show cases / options for structured creativity and innovation. If you are like others, plan on 3 sessions over a 6 to 12 week period, or a weekend "hack-a-thon" / "sprint" on "innovation through diversity and inclusion".
It is important during the group's working sessions, that the facilitator set rules and restrict the Pioneers and Drivers from speaking first.This has the effect of stopping both information and reputation cascades that are poison to inclusion, and a major deterrent to innovation. What Pioneers and Drivers experience in the first sessions - is both funny and revealing - they HATE not being able to speak first, respond with counter arguments, and control the flow of information. (They truly do!) It is been my experience that 16 hours of training/education/theory and experimentation, and then 30 to 45 days of monitored "practice" of inclusive behaviors is enough to cause participants to recognize the difference, the increased inclusiveness, and the more fruitful innovation results. Ofcourse all bets are off if the dominant behaviors are a reflection of a "culture of fear" as opposed to a "culture of courage". A simple 7 to 9 question culture test should reveal that for you. If there is a little too much fear, then different tactics apply.
(You would have guessed right if you are thinking I must run these sorts of programs for large companies. Indeed, I am a Chief Transformation Officer, and I ran one of these last week for a 2,400-person Silicon Valley tech-consumer services firm. Happy to have a chat if a structured, strategic approach based on the science of diversity and inclusion, and its impact on innovation and profit. Good luck!