I am not asking about Site Search. I am wondering how to include a Google search box that searches the whole internet (not limited to a single site like Site Search would be) that also uses the same autocomplete behavior you see on Google.com.
Some of you may remember iGoogle, which was Google's web portal which I used and loved for years until they shut it down last year. I'm making my own iGoogle replacement. I can easily enough add a textbox up top to do the search, but what I'm having trouble reproducing is the JavaScript autocomplete behavior that you get with regular Google.com.
So starting with this:
<form action="https://www.google.com/search" method="get">
<input type="text" name="q" value="" />
</form>
How do I get it to do auto-complete?