You would typically do something like:
protected void btnClose_Click(object sender, EventArgs e)
{
    ClientScript.RegisterStartupScript(typeof(Page), "closePage", "window.close();", true);
}
However, keep in mind that different things will happen in different scenerios.
Firefox won't let you close a window that wasn't opened by you (opened with window.open()).
IE7 will prompt the user with a "This page is trying to close (Yes | No)" dialog.
In any case, you should be prepared to deal with the window not always closing!
One fix for the 2 above issues is to use:
protected void btnClose_Click(object sender, EventArgs e) {
    ClientScript.RegisterStartupScript(typeof(Page), "closePage", "window.open('close.html', '_self', null);", true);
}
And create a close.html:
<html><head>
 <title></title>
 <script language="javascript" type="text/javascript">
     var redirectTimerId = 0;
     function closeWindow()
     {
         window.opener = top;
         redirectTimerId = window.setTimeout('redirect()', 2000);
         window.close(); 
     }
     function stopRedirect()
     {
         window.clearTimeout(redirectTimerId);
     }
     function redirect()
     {
         window.location = 'default.aspx';
     }
 </script>
 </head>
 <body onload="closeWindow()" onunload="stopRedirect()" style="">
     <center><h1>Please Wait...</h1></center>
 </body></html>
Note that close.html will redirect to default.aspx if the window does not close after 2 sec for some reason.