Implementing Google Search in your website

I had to implement the "google search" field in one of my website. What i wanted was to have a search field in home page which would have landed into a search.php page which in turn would have run the google search script provided by google.

What I did was:

Home page:

Search.php

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Some sources:
http://stackoverflow.com/questions/2298027/pass-variable-to-google-custom-search-engine