The first_name and last_name are not being registered in my user model

You're probably using Rails 4 and the course uses Rails 3.2 (it's very old). Whenever you introduce new fields to the models and want them to be editable through forms, you have to whitelist them. This video explains it nicely: http://www.lynda.com/Ruby-Rails-tutorials/Mass-assignment-strong-parameters/139989/159116-4.html

With Devise it's more complicated because there is no overt user controller to put user_params in. Go to devise documentation: https://github.com/plataformatec/devise and scroll down to Strong Parameters section to see how it's done. In your case you should probably add this to your Application controller:

  before_action :configure_permitted_parameters, if: :devise_controller?

  protected

  def configure_permitted_parameters
    devise_parameter_sanitizer.for(:sign_up) << :first_name << :last_name
    devise_parameter_sanitizer.for(:account_update) << :first_name << :last_name
  end

This should allow you to create and edit users properly now. Strong Parameters is something that you will deal with all the time in Rails 4 apps, so make sure you understand the topic thoroughly.

Note: this course may difficult for you if you're using the newest versions of Rails and other gems. A lot of this is deprecated, some of the gems changed, some are not even maintained anymore.