An easy way to expand your conflict resolution ability is to begin using the two step discussion process. This is so simple that you might say, "Isn't it obvious?" Well, no. It certainly wasn't to me for many years. So here's a personal story that shows its power.
In a large institution where I worked, people rolled their eyes about the facilities manager. Kathy had been there for ages and people said she was an inflexible nitpicker. Everyone had a story - we all had to go through her to arrange space and technical support for our meetings and workshops.
Soon after I arrived, I too had my moment with Kathy. I needed access to meeting rooms at unusual hours. This required a special key - which she tightly controlled. I also needed her permission to bring in special equipment.
The two step approach looks like this: Step One: Take steps to establish or affirm the relationship. Step Two: Engage in problem-solving or task activity.
In conflict styles training, you have an option to use either a paper or online version. I used to be ambivalent on this, but no more.
I'm an old-school trainer. I love the simplicity of paper and face-to-face training. But after Style Matters had been out in paper for several years, demand for an online tool drove us to also develop a digital version. That was an eye-opener for me.
After dozens of hours honing our scoring algorithm, I couldn't deny that the score report our server spits out for each user mines the user data in ways I can't match in a workshop from a hand-tallied score summary. It would take quick thinking and 10-15 minutes dedicated to each participant for a trainer to come even close to the detailed insights contained in the 10 page score report generated by our server. That's just not realistic with 10-20 people in a workshop.
So I'm a reluctant convert to the digital version of Style Matters. We still sell the print version, but in my opinion the ideal approach in training is to have users take the online version before the workshop, print out the score report at home, and bring it to a live workshop. (Already, you've saved 20 minutes of group time that would otherwise be spent passing around paper forms, giving instructions, and waiting for everyone to finish!)
Then in a face to face setting take users through a learning experience (supported by this Powerpoint or your own sketch of it) that provides some input on conflict styles, reinforced by review and discussion of digital score reports in small and large group settings.