We've included a whole section on negotiating in our "Guide to Selling", which you should make sure you read and get to know well as it could save you thousands.
In brief, however, knowing the true value of a property allows you to decide the maximum price that you are willing to pay. With asking prices usually set at a level that is 5-10% above the expected selling price this gives you a framework for your negotiations.
Having a framework, which includes your upper price limit, is a great advantage when it comes to negotiating. This is because it takes much of the emotion out of the process and emotion is what leads people into trouble.
The more rapport you have developed with the seller the more likely they are to give you a discount. Above all, take your time and don't allow yourself to be rushed into making a decision.
If yours is the right offer it will be accepted. If, on the other hand, the bidding goes above your maximum price then you know that you've just avoided paying too much. That's why it's so important to work out your maximum price when things are calm and you have time to think, not in the heat of negotiations.