BA Interaction skills cover a wide range of actual competencies, so I'm just gonna hit on the small changes that over the years have had huge impacts, and took very little extra effort on my part to learn implement. Some of them are so simple it hurts, yet so many of us don't do them.
1. First and Easiest, Smile
People under estimate the power of a smile. I can go on and on about why smiling should always be your default when interacting with people, but put simply, people tend to like people who like them. People work better with people they like.
2. Admit When You Are Wrong
This is a tougher one, and sometimes people see it as a sign of weakness in themselves, but this is one of the most powerful tools you can put in your belt. It shows that your are a person of integrity and a person who you'd probably want on your team. The book does a better job of breaking this one down, but trust me, being able to say "I was wrong" makes you way stronger that continueing to fight when clearly you are wrong.
3. Don't Argue
If you think you are right and another person is wrong. The first thing you have to do is get on the same accord as them. Abandon your thinking and jump into their shoes. Really dig in and find out why they are thinking the way they are. If you start by telling someone "I'm right, your wrong and here is why..." then they most likely stopped listening at "You're wrong" and instead of thinking about the validity of your points, they are thinking about how to defend themselves and counter your points. People want to be understood, not told they are wrong, and people are naturally defensive. Take time to understand them, first. Always!