You would think that some people are just born with good negotiating skills. Others, who are good negotiators - have cultivated that skill.
A little incident a couple weeks ago related to my car. Usually, I let little things go - but this time - it was more than little. At first the manager said, "Small mistake - it's just a cosmetic thing - nothing some paint won't fix." But I want a new wheel! The mistake? Had my brakes changed, and they forgot to put the gasket and screw back on to seal the brake fluid line - which ultimately leaked and the acid ate up the paint on my wheels. Never mind the bigger issue of no brake fluid right?!
We couldn't agree on anything - so plan B. Ironically the very next day, I saw this manager in a grocery store parking lot with his cherry-ed out 1956 truck. It was freshly polished, with chrome wheels so sparkling and clear they could have been mirrors. Likely with sarcasm I said, "Wow - imagine if brake fluid spilled on those wheels and ate up the chrome."
Suddenly, we were speaking the same language and landed an agreement about my wheel.
Point about negotiating?
Give your offer the advantage from the get-go - set the bar for what you want with higher expectations yet strong substance. It will set the standard for future discussions.
Speak a different language if you have to - will the person you are dealing with be swayed by hard facts, or do they need to talk and discuss things out? Take the time to understand their language and mirror it - the end result is your offer or request will be more easily received.