<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=”site url here” checked /> only search “site name”<br />
</td></tr></table>
</div>
</form>

************************************************

Google Free web search ……
<!– Search Google –>
<center>
<FORM method=GET action=”http://www.google.com/search”>
<input type=hidden name=ie value=UTF-8>
<input type=hidden name=oe value=UTF-8>
<TABLE bgcolor=”#FFFFFF”><tr><td>
<A href=”http://www.google.com/”>
<IMG src=”http://www.google.com/logos/Logo_40wht.gif”
border=”0″ ALT=”Google” align=”absmiddle”></A>
<INPUT TYPE=text name=q size=25 maxlength=255 value=”">
<INPUT type=submit name=btnG VALUE=”Google Search”>
</td></tr></TABLE>
</FORM>
</center>
<!– Search Google –>

****************************************************

Google Free SafeSearch ……..
<!– Google SafeSearch –>
<center>
<FORM method=GET action=”http://www.google.com/search”>
<input type=hidden name=ie value=UTF-8>
<input type=hidden name=oe value=UTF-8>
<TABLE bgcolor=”#FFFFFF”><tr><td>
<A href=”http://www.google.com/search?safe=vss”>
<IMG src=”http://www.google.com/logos/Google_Safe.gif”
border=”0″ ALT=”Google” width=”115″ height=”45″ align=”absmiddle”></A>
<INPUT TYPE=text name=q size=25 maxlength=255 value=”">
<INPUT type=hidden name=safe value=strict>
<INPUT type=submit name=sa value=”Google Search”>
</td></tr></TABLE>
</FORM>
</center>
<!– Google SafeSearch –>

*****************************************************

Google Free web search with site search ………….
<!– SiteSearch Google –>
<FORM method=GET action=”http://www.google.com/search”>
<input type=hidden name=ie value=UTF-8>
<input type=hidden name=oe value=UTF-8>
<TABLE bgcolor=”#FFFFFF”><tr><td>
<A href=”http://www.google.com/”>
<IMG src=”http://www.google.com/logos/Logo_40wht.gif”
border=”0″ ALT=”Google”></A>
</td>
<td>
<INPUT TYPE=text name=q size=31 maxlength=255 value=”">
<INPUT type=submit name=btnG VALUE=”Google Search”>
<font size=-1>
<input type=hidden name=domains value=”YOUR DOMAIN NAME”><br><input type=radio name=sitesearch value=”"> WWW <input type=radio name=sitesearch value=”YOUR DOMAIN NAME” checked> YOUR DOMAIN NAME <br>
</font>
</td></tr></TABLE>
</FORM>
<!– SiteSearch Google –>

Some other reference site for this…

http://www.fullerton.edu/it/services/Web_Publishing/Google/