How Google has made the process of removing a URL from the results a little easier. You do this through Webmaster Tools.
I'm sure we've all, at one time or another, posted something online which was private or was just incorrect. While changing the page isn't hard, what if you're unlucky enough that a search engine has been round and hoovered up what you've written in the meantime? Don't forget, Google and Bing effectively keep a public copy of the entire web (click the 'cached' link next to almost every Google result). Unfortunately, you'll just have to wait until they come round again. If you have an "XML Sitemap" – and you should – then you can mark the page as high priority, ensuring it gets re-crawled the next time the search engine comes round. But you will have to wait.
Harder than this is getting a page removed from the index completely. Just deleting a page from your site is a hopeless approach; the search engines might take months of crawling and re-crawling your site before they decide that the page really no longer exists. You need to flag the page as having gone, either by redirecting its URL to a replacement page, or listing it as gone, which in Google, you do through Webmaster Tools.
(You have got a Webmaster Tools account, haven't you? Whoever created your website should have ensured you do, as part of the service, or they weren't doing their job properly. But if you haven't got one, sort it out today. It's in week 1 of our Insider Programme, that's how essential it is.)
Now Google has made the process of removing a URL from the results a little easier, and Easier URL removals for site owners on Google Webmaster Central gives the full story. You'll still need – eventually – to properly indicate that the page no longer exists, or block the "Googlebot" from crawling the page, but you can fast-track its removal now.