<form action="http://www.google.com/search" method="get">
<input type="text" name="q" value="" id="textbox" >
<input type="submit" value="Search" name="infield">
<script>document.getElementById('textbox').focus()</script>
</form>
The script at the end of the form is not needed this just sets the cursor to start in the search box instead of the address bar. You may need to mess with the code a little to get it to work. I have had problems when I would copy and paste the code but with a little searching and seeing different ways to write this block of code I have been fortunate to get it to work easily.
Hope this works and is what you are looking for.