How do I Practice the Art of Deliberative Conversation vs. Arguing?

I suggest you read the book Difficult Conversations, by Douglas Stone, Bruce Patton and Sheila Heen. This book is incredible useful and gives practical guidance on how to implement the practice of improving verbal communications.

Here is a quick suggestion. Start with finding a point of agreement. Maybe it is a sales goal your group has to meet. Then address the various suggestions in terms of their ability to meet the goal. Maybe there is no consensus as to which method is likely to work better. Maybe some additional research - facts, not just opinions - will help. And the participants should remind themselves to avoid making it personal.

I would start with watching this, from Monty Python.
http://youtu.be/kQFKtI6gn9Y
:-)

Agree with the above points - find common ground, an agreed goal; use metrics to take out opinion and emotion; check the ego, appreciate the concerns of the other person(s); be willing to examine your own position against the common ground/goal. Check your logic for soundness, stick to it gently but firmly; admit & yield any fault in your thinking. Stay on the high ground, keep the common goals as the objective, not a personal victory.

Look into Coaching techniques. Coaching teaches you how to get to the root cause of an issue really by asking enough probing questions to get the person to realize the issue so you're not just telling them. If a person can self discover the issue they can then take down the defense mechanism and work with you to find a solution. It works in a non attacking fashion where the person really doesn't even know what you are doing. I love it and use it all the time. I even use it when an employee comes to me with "I have a problem and don't know what to do." Ask a lot of why's and how do you think we should handle this problem? Sometimes you have to redirect because they are way off base but there are a lot of times I can simply smile at them and praise their innovative thought process and move on fairly quickly.

Focus on behaviors, not personalities. Make sure you are listening before you ask to be heard. (Stole this one from Covey, I think.) Be factual and make sure both parties agree on the facts. If not, bring in a third party to arbitrate. Don't take the disagreement personally. Sometimes we have to agree to disagree.

Google "deliberative conversation" or "co-intelligence" and you will find sites that discuss the issue. You may also find "public deliberation" to be of use as it discusses the topic/concept that may be applied to a company setting.