How to add a custom search on Google search engine for a website?

How to add a custom search on Google search engine for a website?
For example : while we search for newyork times on Google search the result displays nytimes.com with a custom search box for nytimes on its search results page with a search button named Search nytimes.com - How they do it?

Its maybe Google is pulling the feeds from website's search function.something google do for big ass sites.I'm not sure if there is a exact method to index your search function.

Newnerd,

You cannot add this yourself. It is an extension of Google Sitelinks and is displayed when Google thinks there is a strong possibility that a user wants more refined results. Whether the site is actually using Google Site Search doesn't seem to be a factor.

Search Engine Land covered this back in 2008. You can read the article here http://searchengineland.com/google-debuts-search-within-a-site-search-box-feature-13522

Best,

Shawn