Here In this article, I have used Visual Studio 2013

Go to File > New > Project > ASP.NET  Web Application (under web) > Entry Application Name > Click OK > Select Empty template > Checked MVC (under "Add folders and core references for" option) > OK

Go to Solution Explorer > Right Click on References form Solution Explorer > Manage NuGetPackages... > Search for "Google.Authenticator"> Install > Close.

Step-3: Add a new ViewModel (class).

Here I have added a new class "LoginModel.cs" in our application.
I have added a folder named "ViewModel" first
Go to Solution Explorer > Right Click on Project Name > Add > New Folder > Rename.
 and then added a class "LoginModel.cs" .
Go to Solution Explorer > Right Click on the folder ("ViewModel")> Add > New Item... > Select class under code > Enter class name > Add.

public class LoginModel
{
    public string Username { get; set; }
    public string Password { get; set; }
}

Step-4: Create an MVC Controller.

Go to Solution Explorer > Right Click on Controllers folder form Solution Explorer > Add > Controller > Enter Controller name > Select Templete "empty MVC Controller"> Add.

Here I have created a controller named "HomeController"

Step-5: Add a new action for login to your controller. 

Here I have added "Login" Action to "Home" Controller. Please write this following code

private const string key = "qaz123!@@)(*"; // any 10-12 char string for use as private key in google authenticator
public ActionResult Login()
{
   return View();
}

HomeController.cs

using _2FAGoogleAuthenticator.ViewModel;
using Google.Authenticator;
using System.Web.Mvc;

namespace _2FAGoogleAuthenticator.Controllers
{
    public class HomeController : Controller
    {
        private const string key = "qaz123!@@)(*"; // any 10-12 char string for use as private key in google authenticator
        public ActionResult Login()
        {
            return View();
        }
    }
}

Step-6: Add view for that login action and design.

Right Click on Action Method (here right click on Index action) > Add View... > Enter View Name > Select "Empty" under Template dropdown  > Select the "LoginModel" (created at previous step) under Model class dropdown > Add.
HTML Code

@model _2FAGoogleAuthenticator.ViewModel.LoginModel
@{
    ViewBag.Title = "Login";
}
<h2>Login</h2>
@* Here we will add 2 form, 1 for Login and another one for 2FA token verification form *@
@if (ViewBag.Status == null || !ViewBag.Status)
{
    <!--Show login form here, Viewbag.Status is used for check is already veirfied from our database or not-->
    <div>@ViewBag.Message</div>
    <div>
        @using (Html.BeginForm())
        {
            <div class="form-group">
                <label for="Username">Username : </label>
                @Html.TextBoxFor(a => a.Username, new { @class = "form-control"})
            </div>
            <div class="form-group">
                <label for="Password">Password : </label>
                @Html.TextBoxFor(a => a.Password, new { @class="form-control", type="password"})
            </div>
            <input type="submit" value="Login" class="btn btn-default" />
        }
    </div>
}
else
{
    <!--Show 2FA verification form here-->
    <div>@ViewBag.Message</div>
    <div>
        <img src="@ViewBag.BarcodeImageUrl"/>
    </div>
    <div>
        Manual Setup Code : @ViewBag.SetupCode
    </div>
    <div>
        @using (Html.BeginForm("Verify2FA","Home", FormMethod.Post))
        {
            <input type="text" name="passcode" />
            <input type="submit" class="btn btn-success" /> 
        }
    </div>
}

Step-7: Add an another action (POST method) for verify user credential from database.

[HttpPost]
public ActionResult Login(LoginModel login)
{
    string message = "";
    bool status = false;

    //check username and password form our database here
    //for demo I am going to use Admin as Username and Password1 as Password static value
    if (login.Username == "Admin" && login.Password == "Password1")
    {
        status = true; // show 2FA form
        message = "2FA Verification";
        Session["Username"] = login.Username;

        //2FA Setup
        TwoFactorAuthenticator tfa = new TwoFactorAuthenticator();
        string UserUniqueKey = (login.Username + key); //as Its a demo, I have done this way. But you should use any encrypted value here which will be unique value per user.
        Session["UserUniqueKey"] = UserUniqueKey;
        var setupInfo = tfa.GenerateSetupCode("Dotnet Awesome", login.Username, UserUniqueKey, 300, 300);
        ViewBag.BarcodeImageUrl = setupInfo.QrCodeSetupImageUrl;
        ViewBag.SetupCode = setupInfo.ManualEntryKey;
    }
    else
    {
        message = "Invalid credential";
    }
    ViewBag.Message = message;
    ViewBag.Status = status;
    return View();
}

Step-8: Add an another action for authorized users (here "MyProfile"), where authorized user will be redirected to after successful login. 

public ActionResult MyProfile()
{
    if (Session["Username"] == null || Session["IsValid2FA"] == null || !(bool)Session["IsValid2FA"])
    {
        return RedirectToAction("Login");
    }

    ViewBag.Message = "Welcome " + Session["Username"].ToString();
    return View();
}

Step-9: Add view for the action (here view for "MyProfile" action). 

@{
    ViewBag.Title = "MyProfile";
}

<h2>My Profile</h2>
<h5>@ViewBag.Message</h5>

Step-10: Add an action for verifying 2 factory authentication token.

public ActionResult Verify2FA()
{
    var token = Request["passcode"];
    TwoFactorAuthenticator tfa = new TwoFactorAuthenticator();
    string UserUniqueKey = Session["UserUniqueKey"].toString();
    bool isValid = tfa.ValidateTwoFactorPIN(UserUniqueKey, token);
    if (isValid)
    {
        Session["IsValid2FA"] = true;
        return RedirectToAction("MyProfile", "Home");
    }
    return RedirectToAction("Login", "Home");
}

Step-11: Set Login page as a default start up page.

Step-12: Run Application.