OmniAuthの設定方法が若干変更されてました

gemがプロバイダ毎に別れた為、個別にGemfileに設定する必要があります。
/Gemfile（twitterとFacebookの場合。追記後、$ bundle install 実行）

gem 'omniauth-twitter'
gem 'omniauth-facebook'

/config/initializers/omniauth.rb（今までと同じ）

Rails.application.config.middleware.use OmniAuth::Builder do
  provider :twitter, 'TWITTER_KEY', 'TWITTER_SECRET'
  provider :facebook, 'FACEBOOK_ID', 'FACEBOOK_SECRET'
end

SessionsControllerの作成

$ rails g controller sessions

/app/controller/sessions_controller.rb

class SessionsController < ApplicationController
  def create
    user = User.from_omniauth(env["omniauth.auth"])
    session[:user_id] = user.id
    redirect_to root_url, notice: "Signed in!"
  end

  def destroy
    session[:user_id] = nil
    redirect_to root_url, notice: "Signed out!"
  end

  def failure
    redirect_to root_url, alert: "Authentication failed."
  end
end

ルーティングの設定
/config/routes.rb

  root :to => "home#index"
  match "/auth/:provider/callback" => "sessions#create"
  match "/auth/:provider/failure" => "sessions#failure"
  match "/signout" => "sessions#destroy", :as => :signout

Userモデルの作成

$ rails g model user

マイグレーションファイルの修正→migrate

class CreateUsers < ActiveRecord::Migration
  def self.up
    create_table :users do |t|
      t.string :provider, :null => false
      t.string :uid, :null => false
      t.string :name, :null => false
      t.string :screen_name, :null => false

      t.timestamps
    end
  end

  def self.down
    drop_table :users
  end
end

$ rake db:migrate

/app/models/user.rb

class User < ActiveRecord::Base
  def self.from_omniauth(auth)
    find_by_provider_and_uid(auth["provider"], auth["uid"]) || create_with_omniauth(auth)
  end

  def self.create_with_omniauth(auth)
    create! do |user|
      user.provider = auth["provider"]
      user.uid = auth["uid"]
      user.name = auth["info"]["name"]
      user.screen_name = auth["info"]["nickname"]
    end
  end
end

テスト用
app/application_controller.rb

class ApplicationController < ActionController::Base
  protect_from_forgery
  
  helper_method :current_user
  private
  def current_user
    @current_user ||= User.find(session[:user_id]) if session[:user_id]
  end
end

/app/views/home/index.html.erb

<% if current_user %>
  Welcome <%= current_user.name %>! <br />
  <%= link_to "Sign Out", signout_path %>
<% else %>
  <%= link_to "Sign in with Facebook", "/auth/facebook" %><br />
  <%= link_to "Sign in with Twitter", "/auth/twitter" %>
<% end %>