Here, we are going to create the simple example to create the login form using servlet.
index.html
<form>  
   Name:<input type="text" name="username"/><br/><br/>  
   Password:<input type="password" name="userpass"/><br/><br/>  
   <input type="button" value="login"/>  
</form>  
Here is ajax Sample
       $.ajax
        ({
            type: "POST",           
            data: 'LoginServlet='+name+'&name='+type+'&pass='+password,
            url: url,
        success:function(content)
        {
                $('#center').html(content);           
            }           
        });
LoginServlet Servlet Code :-
    package abc.servlet;
import java.io.File;
public class AuthenticationServlet extends HttpServlet {
    private static final long serialVersionUID = 1L;
    protected void doGet(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException
    {   
        doPost(request, response);
    }
    protected void doPost(HttpServletRequest request,
            HttpServletResponse response) throws ServletException, IOException {
        try{
        HttpSession session = request.getSession();
        String username = request.getParameter("name");
        String password = request.getParameter("pass");
                /// Your Code
out.println("sucess / failer")
        } catch (Exception ex) {
            // System.err.println("Initial SessionFactory creation failed.");
            ex.printStackTrace();
            System.exit(0);
        } 
    }
}