Google-search – How to make a safe search in Google

If you are using the Firefox Google search toolbar, I am not sure how to permanently make that change.

But if you are using the search field (the one that's to the right of the address bar by default), you can write your own search plugin fairly easily.

Following the example on that page, you would put the QDR parameter (as described in another answer) in like so:

<search 
 name="Google: Past Year"
 method="GET"
 action="http://www.google.com/search"
 queryCharset="utf-8"
> 

  <input name="q" user>
  <input name="qdr" value="y">
</search>

A basic description of how Google Web History works: http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=54068

[...]

Note: Depending upon whether or not you're signed in to a Google Account when you search, the information we use for customizing your experience will be different:

Signed-in personalization: When you're signed in, Google personalizes your search experience based on your Web History. If you don't want to receive personalized results while you're signed in, you can turn off Web History and remove it from your Google Account. You can also view and remove individual items from your Web History.

Signed-out personalization: When you're not signed in, Google customizes your search experience based on past search information linked to your browser, using a cookie. Google stores up to 180 days of signed-out search activity linked to your browser's cookie, including queries and results you click.

To change Web History settings for your account go to: https://www.google.com/history/