Sign into AdSense and look for the resources then on the lower right of the page look for Reference Links and under that look for Publisher tools. You will eventually find the code to generate the search box just for you. It is a form.
If you have the code then you paste it in the html source of your webpage. You have to have control of a webpage to do that. You can't, for instance, put the search engine on Hubpages.
You need your own webpage. You can see an example of my personal site with a search box down the page at http://ButchNews.com