When the first request comes, Set a flag in Session. Reset this flag only after the processing of the first request completes.
If the user requests again, without having the first request completed, just reject the request by returning from ProcessRequest() without any further line of code executed. Additionally you can reply the user back with appropriate status-message.
EDIT
using System;
using System.Collections.Generic;
using System.Text;
using System.Web;
using System.Web.SessionState;
namespace MyHandlers
{
public class MyHttpHander : IHttpHandler,IRequiresSessionState
{
public bool IsReusable
{
get { return true; }
}
public void ProcessRequest(HttpContext context)
{
context.Response.Write("<h1><b>HttpHandler Test</b></h1>");
context.Session["Test"] = "Invoke a session in HttpHandler.";
context.Response.Write(context.Session["Test"]+"<br>");
context.Response.Write("<a href='HttpHandlerCsharp.aspx'><b>return</b></a>");
}
}
}