Setting a 404, best practices
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Is it enough to just delete a page, or is it necessary to do something else to 404 a page correctly?
Is there a great link to explain how to set http status codes?
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If for any reason a web page is not found your web server will return a 404 http header code. Wikipedia offers a very readable status code list:
http://en.wikipedia.org/wiki/List_of_HTTP_status_codes
The challenge you are facing is Google does not automatically de-index a link due to receiving a 404 error. At times Google might crawl a site and there can be an issue where a page is not available, or even your whole site. In my opinion the best way to handle that is for Google to wait until they have received a 404 response a few times, then remove the page.
Make sure your page is not blocked by robots.txt or else Google will never be able to see the page and know it is 404'd.