For me, the key point of Getting To Yes is to focus on outcomes not positions. Outcomes are what we want to accomplish, for example "getting something to eat". Positions are a single concrete instantiation of that outcome, for example "getting a cheeseburger at Burger King".
A problem with humans is we often get very attached to achieving our position, even though there are several positions that can achieve our outcome, many of which will make other people happy. When we get in a fight with someone it's usually because we have incompatible positions, not incompatible outcomes. If we can refocus our interaction onto achieving outcomes, we can usually find a position that can make everyone happy.
A few days after reading Getting To Yes, I was at the cafeteria and had an excellent opportunity to practice what I'd been reading:
Igor: "Can I get a coffee?"
Barista: "Sorry - we're closed, we won't open for 20 more minutes"
Igor: "I see you're closed, but can I get a coffee anyways?"
Barista: *Confused Look*