I'm going to assume that virtually everyone reading this either has or had a spouse, partner, significant other or best friend-- in other words, anyone that you share an emotional bond with. I'm also going to assume that at some point in that relationship (probably many times) something you said was misunderstood. You thought you were being incredibly clear, but you're the listener was wildly off the mark in understanding what you meant. I'm sure that's just as true the other way around.
You've also probably had experience making your case to someone that you're not that close with--a boss, direct reports, customers, prospects, the media, and many others. They, in fact, could be someone you've never met before. And since they don't know how you think, what you're life is like, your past experiences, or the way that you typically communicate, it's even more likely that they may not get what you're talking about.
So, how then do you make sure that your message is getting across the way you intended and not misunderstood? By constantly interpreting you.
Almost every time you make a statement, you need to add more. Following your declarative sentences, you should say things like, "Here's what I mean by that" or "Here are the implications of what I'm talking about" or "Here's how I came to that conclusion" or "Here's how this changes things." Offer examples, illustrations, or stories that create a picture of what you mean. Narratives create a mental image for the listener. You want them to say (at least to themselves) "I see what he's talking about." Stories have the added bonus of being more memorable than a simple flat-out statement.
Another technique to achieve clarity and understanding is to ask and answer your own questions. This is especially important if there is anything challenging or negative in what you're proposing. "If I were sitting where you are, I might be wondering..." or "Some people want to know how can that be...?" By bringing up the tough questions, it demonstrates that you're not afraid to handle any controversial issues stemming from what you're offering. It gives you credibility. It also gives you a chance to control the conversation.
One of the best ways to speak clearly is to truly understand the people you are talking to. Who are they? What do they care about? How deep is their knowledge of your subject matter? When you understand them and what life is like from their point of view, you can tailor your remarks so it truly connects with them.
It all gets down to something Bill Clinton once said: "Explanation is eloquence."