Like this
<form method="get" action="http://www.google.com/search">
<div style="border:1px solid black;padding:4px;width:20em;">
<table border="0" cellpadding="0">
<tr><td>
<input type="text" name="q" size="25"
maxlength="255" value="" />
<input type="submit" value="Google Search" /></td></tr>
<tr><td align="center" style="font-size:75%">
<input type="checkbox" name="sitesearch"
value="askdavetaylor.com" checked /> only search Ask Dave Taylor<br />
</td></tr></table>
</div>
</form>
For displaying the results in a separate frame, you have this site as an example.
That would be something along the lines of:
<html>
<head>
<meta http-equiv="Content-Language" content="en-gb">
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
<script language="javascript" type="text/javascript">
function showFrame () {
var e = document.getElementById("if1");
e.style.visibility = "visible" ;
}
</script>
</head>
<body>
<p> </p>
<p>
<span id="spSearch" onclick="showFrame()">Search</span>
</p>
<p> </p>
<p><iframe name="I1" id="if1" width="100%" height="254" style="visibility:hidden" src="http://www.google.co.uk">
Your browser does not support inline frames or is currently configured not to display inline frames.
</iframe></p>
</body>
</html>