LuhnyBin - my first Ruby script
Welcome to ruby :), here are a few changes you might want to consider.

#!/usr/bin/ruby

class LuhnyBinChecker

  def initialize(number)
    @number = number
  end


Try to keep your methods pure without i/o, and collect the i/o in some portion that is dedicated to it. It helps later while you refactor the code. It is also nicer to not to rely on member variables too much, and preserve the referential transparency of functions where possible.

  def check
    arr = digits(@number)
    puts "Checker: doubling every second number from the right.."
    arr = doubleSecond(arr)
    puts "Checker: calculating the sum.."
    getResult(sumNumbers(arr))
  end


Always be on the lookout for things you can refactor and reuse.

  def digits(n)
    n.to_s().scan(/\d/).map{ |c| c.to_i }
  end


Two ways of doing the doubleSecond, I prefer the second way, and I think that is a more ruby way. But as a beginner, you might understand the first better. Choose which ever you like.

  def doubleSecond(arr)
    #arr.each_with_index do |item, i|
    #  arr[i] = arr[i] * 2 if (i %2 == 0)
    #end
    arr.zip((1..@number.length).to_a()).map do |e|
       e[1] * ((e[0] % 2) + 1)
    end
  end

  # treat numbers &gt;= 10 individually 
  # e.g. 12 -&gt; 1 + 2 = 3
  def sumNumbers(arr)
    arr.map{|i|
        i &gt; 9 ? splittedSum(i) : i
    }.inject(0,:+)
  end


You can think of Array.inject(0,:+) as Array.sum()

  def splittedSum(number)
    digits(number).inject(0,:+)
  end

  def getResult(sum)
    sum.modulo(10) == 0
  end
end


It is nicer to have a guarantee that a CreditCard will always contain a number rather than to check for nil in the getter method.

class CreditCard
  attr_reader :number
  def initialize(number)
    @number = number
  end

  def verify
    (LuhnyBinChecker.new(@number)).check
  end
end


You can use abort if some conditions fail to satisfy.

if __FILE__ == $0
  puts "Please enter the credit card number to check:"
  input = gets()              # input card number
  abort "Please enter only numbers." if input !~/(\d+\s)+/
  card = CreditCard.new(input)
  puts "You entered: " + card.number
  puts "Verifying card number now..."
  if card.verify()
     puts "Credit card number is valid"
  else
     puts "Credit card number is valid"
  end
end