How to validate the date such that it is after today in Rails?

Your question is (almost) exactly answered in the Rails guides.

Here’s the example code they give. This class validates that the date is in the past, while your question is how to validate that the date is in the future, but adapting it should be pretty easy:

class Invoice < ActiveRecord::Base
  validate :expiration_date_cannot_be_in_the_past

  def expiration_date_cannot_be_in_the_past
    if expiration_date.present? && expiration_date < Date.today
      errors.add(:expiration_date, "can't be in the past")
    end
  end    
end