This article offers advice on how to negotiate the purchase of a domain name that isn't currently listed for sale. If a domain name is already listed for sale somewhere then generally be prepared to pay the asking price.
Before you start, note down what you think is a reasonable price to pay for the domain name and determine the maximum price that you'd be willing to pay. It's important to realise that what you think is a reasonable price might not be consistent with what the domain name owner is prepared to sell for, especially if they're already making good use of the domain. Some domain names make a substantial monthly income just from running PPC ads and any domain name owner in their right mind wont sell off a steady income stream for too cheap. Always be polite even if the seller's price is way over your maximum budget. See our article on domain name pricing if you're unsure where to start.
Try to determine who the owner is. Are they a domain name speculator? Are they a company using the domain name to run their business? Are they a hobbyist running a low-key website or are they perhaps an individual who registered the name for their own personal site. All of these different types of owners vary in experience, motives, and minimum price they're likely to accept. The approach you should take, and your expectations, depend on who the owner is. For instance if you're trying to buy a domain name currently used for a hobby site then maybe compliment the site and imply that you'd like to keep the site going after purchasing the domain name or offer that you'll provide a link to the hobbyist's new domain name on your website should they sell to you. If the owner is a company operating a website for their business then realise that they're unlikely to sell whatever your price is unless you'll also consider purchasing their business or a component of it. If you're dealing with a speculator then they'll probably have more experience in the domains business than you do but at least they're driven by economics rather than having a personal attachment to a name so they'll virtually always be prepared to sell if the price is right.
If you're representing a large or well-known company, try not to reveal who the company is, at least until a price is agreed on. Maybe use a personal email address or have a friend make the initial inquiry, but don't resort to outright fraudulent statements or methods.
It's common to make an initial inquiry by email as to whether the domain name is for sale and if so, what price the owner would require. While this is a cheap and easy way to make first contact with the domain name owner, it is not necessarily the most effective; your email might be nuked by the owners' spam filters and even if it does get through it might be ignored since the owners of popular domain names are often bombarded with low-quality offers to buy their domains. A more effective, though more expensive way to begin your negotiations is to have a lawyer or accountant send a registered letter to the domain name owner stating that you're interested in purchasing the domain name and offering a reasonable price up front.
Don't offend the seller by offering a very low price. If you waste their time then they're likely to up their price. Generally be prepared to offer at least 1/3 of your maximum price up front, or more if the domain name has an established website with a real business behind it. Don't even think about offering less than $300 unless the owner is clearly an amateur.
If anonymity is of importance or if you're concerned about making a mistake then consider using a domain broker to act on your behalf.