[WebMethod]
        public static string SetSession(string name)
        {
            HttpContext.Current.Session["Name"] = name;
            return "Hello " + HttpContext.Current.Session["Name"] + Environment.NewLine + "The Current Time is: " + DateTime.Now.ToString();
        }


<script type="text/javascript">
    function SetSession() {
        var name = document.getElementById("<%=txtUserName.ClientID%>").value;
        var request;
        if (window.XMLHttpRequest) {
            //New browsers.
            request = new XMLHttpRequest();
        }
 
        if (request != null) {
            var url = "WebForm3.aspx/SetSession";
            request.open("POST", url, false);
            var params = "{name: '" + name + "'}";
            request.setRequestHeader("Content-Type", "application/json");
            request.onreadystatechange = function () {
                if (request.readyState == 4 && request.status == 200) {
                    alert(JSON.parse(request.responseText).d);
                }
            };
            request.send(params);
        }
    }
    </script>
    <asp:TextBox ID="txtUserName" runat="server"></asp:TextBox>
<input id="btSet" type="button" value="Set Session" onclick="SetSession()" />