Sessions aren't client side, they are Server side - as is all C# code. Only Javascript is executed at the client, C# and VB are always executed on the server and have no direct access to client resources.
So to access Session variables on the server side is trivial:
string userName = Session["Name"].ToString();
You can access Server variables on the Client side in Javascript:
<script type="text/javascript">
function showName() {
alert('<%=Session["Name"].ToString() %>');
}
</script>