To make your conversation more effective doesn't require a complete overhaul.  A little tuning up will do a lot.

Here's a small 2-part technique that can help when a disagreement arises:

Your conversation partner brings up a contentious issue such as the health care reform bill now being considered by the congress.  S/he goes on at some length, and you disagree.

A typical response would usually be of the "Yes, but" variety.  Notice that the "but" is the equivalent of a "no" and invalidates what the other person says.

Instead, try this:

1. Accurately summarize what your partner has said.  This gives  evidence that you heard accurately, and it is respectful. Moreover, if your summary isn't accurate, your partner can correct it by saying "No, that's not what I meant to say.  What I mean is . . ."

2. Then say something like "I have a different viewpoint. My thinking is . . ."  Or, "My understanding of that issue is somewhat different.  I've come to the conclusion that . . ." Or even, "Interesting.  I get your point.  My story about that issue is . . ."

Listening carefully, then summarizing the other's ideas before sharing your viewpoint increases the possibility that s/he will also listen to you.  No guarantee, of course, but you have a better chance that the other person will reciprocate.

Then, identifying your ideas as "my viewpoint" or "my story" is more accurate.  Neither of you has the absolute truth.  Instead, both of you have opinions based on what you've heard and read.  I have found that describing your ideas as MY viewpoint (at this time) rather than THE TRUTH makes a conversation more flexible and less contentious. 

That's the minor change, the "two-step."  First, summarize (accurately paraphrase) and make any needed corrections. Second, deftly offer your differences as "my viewpoint" or "my story." 

I think you'll find that very often this minor change will result in a major positive difference of better listening and more civility.  You will be disagreeing without being disagreeable.