you need to put that text field into a variable and pass it through as a link.
I'm not sure googles format for their search string, but the way you'd probably want to do it is as form with a "Get" style
<?if($_GET['submit'])
{
header("location:http://google.com?variable='$_GET[searchstring]';?>");
}
else
{ ?>
<form name='form1' method='get' action='test.php'>
<input type=text name=searchstring>
<input type=submit name=submit>
</form>
<?}?>
This is a very rough idea, I havn't tested it, but should give you an idea of the structure you need to follow. First you need to open the form, then fill it out, when it's submitted you than need to create link based upon it, and then automatically go to that link.
this is a dirty way of doing it i beleive. I'm sure there are others who can do it better.