I assume you're trying to just purchase the URL (as opposed to the content and intellectual property of the website as well two).

How you going about buying the URL depends on whether the owner of the URL is a hobbyist or a financial speculator. If you the owner is a hobbyist, it's best to reach out to them and establish a relationship with them before offering to buy the URL. Getting to know them will improve the likelihood of a deal happening since they might not be 100% driven by getting the highest purchase price.

If the owner of the URL is a financial speculator, it might make sense to use a 3rd party domain buying service. This way you reveal as little possible information to the seller about your intent and ability to pay. Also, if negotiations sour you can try again later.

I'm always surprised at how irrational domain owners can be. A lot of them refuse to be contacted with offers, even if they're not using the domain. You'd think there would have to be a price at which they'd be interested!

Also, probably obvious, but the whois registration info will often have a contact email.