Earlier this month I talked about the ECJ ruling against Google on the “right to be forgotten."
Google has now set up a web form and process for making these requests. You need to provide your name, the URLs you want hidden, and an explanation of why the URL is "irrelevant, outdated, or otherwise inappropriate”.
Google will then make the call about whether your request will be honored. They will "assess each individual request and attempt to balance the privacy rights of the individual with the public’s right to know and distribute information. When evaluating your request, we will look at whether the results include outdated information about you, as well as whether there’s a public interest in the information—for example, information about financial scams, professional malpractice, criminal convictions, or public conduct of government officials."
Remember, this only removes that URL from Google searches for your name, not from other searches, other search engines, or from the underlying website.