As someone who has worked in the field of sustainable business change for 27 years, it's critical to have curiosity, passion, and current and projected data specific to the audience you're trying to educate, influence, or get confirmed support from.
Genuine curiosity will do two things - connect you in a very real way to your target audience. Ask them what's important to them, what risks or benefits they need to avoid or want, A finance department will have very different needs that need to be presented in their unique language than someone in design or a CEO. Understanding their unique language will help you eliminate much of the typical miscommunication that happens when trying to present (not argue unless you're talking about debate or court) your case; it also shows the audience that you clearly have taken the time to get to know them and what they need.
Passion and storytelling is the powerful context behind the data. How the data might affect people or organizations or the planet told from an individual's or group's or your perspective. Passion also infuses your "argument" with compelling emotion, which when coupled with data (current and projected) gives everything more depth and richness and might provide the tipping point for one or more members of the audience. People, no matter how analytical or creative, crave connection - it's good to keep that in mind. But you need data too.
Data - you need it. And you may need to present specific "what if" scenarios to show them projected futures. For example, if you worked for Nike or Adidas and were trying to get a Restricted Substance List approved and implemented, you would need to show them how much money it's cost either their company in the past or a comparable company, thus illustrating how much money could be saved and invested in the future or how much money could be lost along with a trashed brand reputation and potential recalls (with associated financial projections) as well as what it may do to stock prices.
In my opinion, what has worked best for me is to do the following:
1. Personal/compelling opening with maybe one piece of data or an explanation of what your going to show them and why it matters to them - by the end of our conversation, you'l understand how we can protect and enhance our brand or contend with product recalls, reduced sales, potential lawsuits, etc. You will already know their language and have their numbers.
2. Show them data and weave in storytelling about how this data could change on a dime and that it may not affect just your company, but your supply chain and the people in it, or the limited amount of fresh water, or your consumers.
3. Illustrate how your solution could make or save them X dollars, consumers, etc.
4. End with a personal close. "One reason I chose to work for X was their passion for sport or health or whatever is relevant. Our brand is about life, athletes in peak performance, and winning. To put those things in jeopardy goes against everything our brand stands for.and frankly puts everything and everyone at risk. It's a small investment to avoid an outcome that could be more costly than you can imagine." Leadership comes in many forms, and I think we have the opportunity to redefine this, eventually making it an industry standard that we adopted first and offered for free.
Long winded answer. If it didn't answer your question, please let me know.
