client side set hiddenfield value and that hiddenfield value how to use in server side

I do not understand where you are having issue but this should just work fine:
Note that I am using jQuery syntax as you have tagged jQuery in the question.

<asp:HiddenField ID="HiddenField1" runat="server" />
<script type="text/javascript">
    $(document).ready(function () {
        $("#<%=HiddenField1.ClientID %>").val("NewValue");
    });
</script>

In the code behind, you can access the control by it's id like below:

string hiddenFieldValue = HiddenField1.Value;

Hope that helps!