Cajun and I, although are not practicing Poly at the moment, have always had an amazing ability to communicate with each other. And this is not just coming from me, this comes from our friends, family and even our couples counselor and my psychologist. He and I know that we can talk to each other about anything and that the other will not jump to conclusions or "go off".
Part of this is because neither of us "fight", we don't yell, we don't fly off the handle, we think and we talk and we ask questions. Another part of it is that we trust each other to be honest and we don't play the games that a lot of couples play such as, "I'm not going to tell him/her what's wrong unless they ask." or ask many times.
Some friends of our gave us an awesome book called All About Us by Philipp Keel
for our wedding. This book is a giant quiz/fill out book meant for two but it can still be useful for 3 or more people I imagine, they just don't have the lines in the book for the extra people. But what the book gets you to do, if you do it together, is to answer questions, some simple, some silly, some hard and some scary even, and open up discussions with each other. One of my favorite questions is in the first chapter along with the basic names, ages, etc. "Would you mind looking at each other for one minute? Yes or No? If Yes, put this book away." We have another set of married friends who absolutely cannot "do" this book. They cannot communicate because they do not trust each other or themselves. Makes me sad. What this book helped us do is explore areas that we had not really communicated about before. It may not teach you how to communicate but it will help to open up about things that are important to discuss in a relationship.
To make this seem less like an ad for the book, effective communication requires trust, calm heads or at least the ability to say when to take a break before things escalate to a fight. Deliberation not argument. Thought not reaction, or if there is reaction first, then think about why that particular reaction. It also requires knowledge of the people involved in the communication effort.