you just need to create the form on the page, and set the action of the form to post to the results page:
<form id="form1" method="post" action="results.php">
<input type="text" name="keyword" id="keyword" />
<input type="submit" name="button" id="button" value="Submit" />
</form>
you can add this form to all of your pages, and each one will post the keyword search term to the results.php page.