Hi,

I would add Google search in my website to display results using "search site".

something as the following website
http://ytbizblog.blogspot.com/2009/08/promoted-videos-now-appearing-on.html

in the above link, if we add any keyword (try to add youtube in search box in the right "Search our Blog") and press go, the results will be displayed in the same website.

any idea for how to implement this using HTML and javascript??

look at google ajax search api
http://code.google.com/apis/ajaxsearch/