All you basically have to do is open up your search template and cut it down to size until you get it to how you like it. I have placed a cut down version of the form that search.php uses below, I hope this helps you in some way, or at least directs you in the right way

.
If you will look on the form, you will see that the action is set to: action="search.php" - You will need to change that to reflect the URL to search.php if you plan on using this on a non-php page.
Code:
<form action="search.php" method="post">
<input type="hidden" name="s" value="$session[sessionhash]">
<input type="text" class="bginput" name="query" size="35"><br>
<input type="hidden" name="action" value="simplesearch">
<input type="submit" class="bginput" name="Submit" value="Perform Search" accesskey="s">
<input type="reset" class="bginput" name="Reset" value="Reset Fields">
</table>
</form>
Hope this helps,
SaintDog