1. Keep it civil.
I wrote a post What NOT to do in a Real Estate Transaction waaaay back in January of 2008. I think my favorite line of that post was "never start negotiations with an opening salvo to the other party." Look, you don't have to be friends with the other party, but keeping the dialog civil, on-task, and moving forward is going to accomplish your goals. Once the other party hates you, it's difficult for them to remove the emotion to work through the deal. Antagonistic negotiations often de-volve into fighting over trashcans and a $30 bathroom mirror (I've seen it happen).
2. Learn the Serenity Prayer. Repeat as necessary.
You can't control the other party, you can only control your end of the deal. People have complex lives going on, with motivations, finances, and weird dynamics that you never will, nor would want to, understand. Trying to figure out the other person, while good for hours of discussion, usually isn't very productive. Take a look at the offer, figure out how to make it acceptable to you, turn it back over to them and let them do the same.
3. Take the time to remove the emotion.
It's VERY typical to get emotional during negotiations. Heck, even I get irritated when I sell my fix & flip properties. It's ok. It's human. You're on opposite teams in this game. So, while you can rant and rave about how CHEAP the Buyers are being, or how NITPICKY the home inspector was, take the time you need to remove that from your response. Usually, by the next morning, you can look at the situation with a clear mind. Take the time you need to think things over, because you might regret losing a workable deal by telling someone to go pound sand.