Adding a search box to your HTML or other pages outside your application is simply a matter of adding this HTML to your pages. Make sure the form action is set to the page containing the SearchResult control.

Example:

<form name=search action="searchresults.aspx">
<table border=0 cellpadding=0 cellspacing=0>
    <tr>
    <td>
        <input type=text name=QueryExpr size=22>
    </td>
    <td>
        <input type=submit value="Go">
    </td>   
    </tr>
</table>
</form>