I usually try and put myself in the shoes of the type of reader of this article and what their motivations are when reading the website or the specific news piece. This is nothing different than what a marketer would do before placing advertising within any media. This game works well when you are in specific sections of the site on specific articles.
Here is a simple example: I read an article about a bicyclist that was struck by a car and killed in the Washington Post today. It was a quick story and pretty sad. But as a media buyer what would a consumer of this article want in support of the article, or even as a compliment to the story? Probably information about bicycle safety? How about an ad about equipment that protects you when you are riding your bike? Or even a link to safety items for your car? Worst case ads for financial services or things that might be relevant to someone that is interested in this type of story.
Well, the ads that showed up? Ads for dial-up internet services. Why you say? I am sure the keyword was traffic, service, and speed. Some marketer thought they would buy these two keywords, because when you search on them on Google it is probably pretty certain you are looking for online net access.
Well, in this case the keywords are not relevant, unless the ad was ‘Work at home and be safer!’