Regular Expression to remove blank lines
What follows is a fairly harsh critique, but I'm hoping that that's what you're looking for as you seem to want to improve you ruby and programming style. Ruby is a lovely language, but getting to know it takes some time - eventually you'll realise that just about everything you write used to take twice as many lines. So, a few pointers:

Variables

Generally in ruby normal variables are underscored. So instead of aVariableName you should probably use a_variable_name. Both will work, but the latter would fit the Ruby style better.

Additionally you choice of variable names seems to go from overly verbose to the opposite. Some are great, but others leave my guessing.

For example where you write:

reader = File.read(input_filename)


I would prefer to write:

in_file = File.read(in_filename)


Functions

Like your variables, the naming of your functions could do with a touch-up. Your functions do not make use of the implicit return that Ruby offers, something that is often considered a better practice.

For example where you write:

  def  remove(stringToremove)

    regEx = /^[\s]*$\n/

    stringToReturn = stringToremove.gsub(regEx, '')
    stringToReturn.strip!

    if stringToReturn.length &gt;= 1
      return stringToReturn
    else
      return ""
    end
  end


In this regard I might have written:

  def remove(stringToremove)

    regEx = /^[\s]*$\n/

    stringToReturn = stringToremove.gsub(regEx, '').strip
  end


Also on your initialize function you include brackets in the definitions this is not required, and is discouraged. Additionally you don't need to include a initializer if there's nothing for it to do.

Rubyness

Some things you might want to consider further as you do more programming in ruby are:


Chaining. For example you can do a_string.gsub("some", "substitution").strip.reverse and other such things all in one line and still keep readability high. Obviously there's a point where it's too much, but that's your judgement.
Your code formatting is a bit out. In a lot of places you seem to be using extra spaces. For example you class definition is class  BlankLineRemover and should really be class BlankLineRemover. You might be using soft-tabs here, and if that's the case - please don't.
You spacing is also very generous. Unless you're separating code into particular chunks then you can skip a few newlines.
This is a real nit-pick, but generally using .size is considered better than .length.


Rewrite

Here's your main class rewritten the way I would have gone about it.

class BlankLineRemover
  def run(in_filename, out_filename)
    File.open(out_filename, "w") do |out_file|
      out_file.write clean(File.read(in_filename))
    end
  end

  def clean(input)
    input.gsub(/^[\s]*$\n/, "").strip
  end
end