Google Ajax Search API

The Google AJAX Search API lets you put Google Search in your web pages with JavaScript. You can embed a simple, dynamic search box and display search results in your own web pages.

Simply sign up for an API key at http://code.google.com/apis/ajaxsearch/signup.html and you can add a Google AJAX Search module to your site.

Going through the few examples at http://code.google.com/apis/ajaxsearch/documentation/ would be sufficient for the headstart.