Focus on making the discussion a collaboration. Consider asking how the other person would like to handle the conversation, and be ready to ask about the range of salaries, why and when they adjust salaries. Have questions ready so you can learn as much as possible. Go into the discussion already having thought about how much time you would need to consider an offer. Practice is the best thing you can do to feel comfortable.
Role playing with a friend can do wonders to improve competence and confidence.
Try different scenarios, but be sure you don't memorize scripted answers. You should go into the negotiation confident that you can follow the conversation wherever it might go. Some people like to see a movie, some like to exercise. Putting yourself into a situation where you're poised and balanced usually helps you perform at your best.