Logging in Ruby on Rails in Production Mode

I would like to view some variables in controller, it tried the following:

Rails.logger.debug "Year: #{Time.now.year}"

puts "Year: #{Time.now.year}, Month: #{@month}"

where can I see the output for Logger or Puts in production mode? Do I need so set something up to view these somewhere?

The normal log level in production is info, so debug logs are not shown.
Change your logging to

Rails.logger.info "Year: #{Time.now.year}"

to show it in production.log.

Alternatively (but not a good idea) you can raise the logging level in /config/environments/production.rb:

config.log_level = :debug

Update Rails 4.2:

Now the default debug level in all environments is :debug (as @nabilh mentioned).
If you want you production environment less chattery, you can reset your log level in /config/environments/production.rb to the former :info:

config.log_level = :info

While I believe @martin-m is right that you probably don't want to clutter your logs by using config.log_level = :debug in /config/environments/production.rb, I believe the default logging level in all environments is debug as of Rails 4.2. So debug logs (and all levels up) will be shown in production unless you specify otherwise.

So in response to your question, you can now write:

Rails.logger.debug "Year: #{Time.now.year}" and see the results in /log/production.log.

See here for more detailed documentation. Here is the documentation for Rails 4.1 for comparison.

If you have a production app that you may need to temporarily change log levels, you might want to use an environment variable to be able to set level without modifying code and redeployment, though your app would need to be restarted, you could take this approach:

config/environment/production.rb

MyApp::Application.configure do
#...
  log_level = :info #default state
  [:debug, :info, :warn, :error, :fatal, :unknown].each do |level|
    if ENV['LOG_LEVEL']&.to_sym == level
      log_level = level
    end
  end
 config.log_level = log_level
#...
end