Google Adsense search – replacing default search

I want to replace the default search with a Google Adsense search.
The Theme I’m using is Amazing Grace

Looking for best practice or what works best for you (those that are already using google adsense search). I would like the search results to keep the user on my website or return the results to my website.

Currently tinkering with Easy Adsense plug-in. Nowhere done and not yet sure if this is the solution I’ll use…

Also some of the info I’ve seen references the need for a search.php and searchform.php. My particular theme only has search.php.

Thanks in advance!