How to

1 - Create reCAPTCHA account.

2 - Add gem 'recaptcha'

# Gemfile
gem "recaptcha", require: "recaptcha/rails"

# DON'T omit "require" option like this!  'gem "recaptcha"'
# This cause the error such as:
# "undefined local variable or method `recaptcha_tags' "

3 - Add validation to controller

# app/controllers/some_controller.rb

def create
    @user = Some.new user_params
    if verify_recaptcha(model: @some) && @some.save
      redirect_to account_login_path, notice: 'Success!'
    else
      render :new
    end
end

4 - Add reCAPTCHA tag in view file (in this case, edit haml file)

# app/view/some/new.html.haml
= form_for user, url: path do |f|
  = recaptcha_tags # ADDED

5 - Add reCAPTCHA config file

# config/initializers/recaptcha.rb
Recaptcha.configure do |config|
  config.site_key  = 'Your Public key'
  config.secret_key = 'Your Private key'
  # Uncomment the following line if you are using a proxy server:
  # config.proxy = 'http://myproxy.com.au:8080'
end

6 - Bundle install and start server

bundle install
rails s

7 - Error massage translation

# config/locale/ja.yml
ja:
  recaptcha:
    errors:
      verification_failed: "認証に失敗しました"
      recaptcha_unreachable: "接続に失敗しました"

It is very easy way to integrate reCAPTCHA to your Rails Application.
Should Try!
Feel free to comment or ask Question.

2017/02/14 fixed chapter "5 - Add reCAPTCHA config file". Thanks to @besukosan