A negotiation is a dialogue between two parties in which both are seeking something from each other. The negotiation is the process of reaching agreement. You want what you want and they want what they want. The best outcome all round is that you both get what you want. The level of success you achieve over time depends very much on how you approach the task and how much you follow your real intent. So many negotiations break down and lead to a lose lose as people get personal and start to battle for victories that are nothing to do with the original intent of the negotiation.
It sounds simple but the most important step in a negotiation is to know exactly what it is you want to achieve. There is usually a range of acceptable outcomes. You get everything and they get nothing is one that usually sets you up for future failure with the other party. A level of compromise acceptable to both giving both of you more than the minimum acceptable to each is the middle outcome. Both getting everything you want is the dream ticket. Write down what it is you want and give some measure to the range of outcomes acceptable to you. Keep this written objective with you throughout your negotiation. When you get distracted by rivalries and emotions you will need to keep referring back to this and check in that you are still seeking what you want.
An equally important step is to understand as clearly what the other party wants out of the negotiation. You should also write this down and even clarify it with them so you can be as clear as possible about what they are after. Before getting in to the process of give and take that leads to a good negotiated settlement you now need to consider how much of the other parties needs you can meet at no cost to you. It is so powerful if you can give them what they want at no cost to you and will position you for success with your needs if you meet theirs first. It is more common that there are trade offs and there will be some costs to giving them what you want. Understand what they are and know which ones you can afford to pay. Also understand which ones you will pay for in return for more of what you want.
You are now ready to negotiate. The more you can focus on giving the other party what they want first either as a good will gesture or as a trade for what you want the more you will succeed. A good will approach is very powerful. If you give someone something for nothing it often creates an obligation on them to give you something back. There is risk in this but if it is worth taking do it as you will get much more than if you go for a straight trade. This is particularly true if you have to negotiate often with the other party.
Whenever it gets tough pull out your piece of paper with what you want and what they want written down on it. Get the negotiation back on to this and more often than not you will get what you want out of the negotiation.