Google Custom Search plugin allows you to add a search box to your site for a custom search provided by Google and shown in your own blog. The advantage of using this plugin is that the search results will be provided by Google and their great search engine. The results are drawn from only the websites you specify when setting your search engine up at Google. You will also be able to earn money from the ads Google shows in the search results.
What you need to do:
The engine ID is the last in the Basic Information section: