How could the Euro zone be broken up in an ordered way? Let’s assume that the members of Euro zone all agreed that it would end in 18 months time with each country getting its own currency.

What process could be put in place to allow this to happen without causing of lots instability?
No Time To Argue

Most importantly, there cannot be an "18 months period of notice". Tt has to be decided suddenly and there cannot be any period in which individuals could respond to the new plan by withdrawing their money and moving cash from one of the member countries to any of the others.

New Currencies

Each country has to have its own currency. These currencies should be free floating against each other, which on the other hand means that some will value up and some down. That is, Germany's new currency will probably value up against whatever Greece will have.

Capital Controls

Therefore, it will be of higher value to have your Euro exchanged for German money than for Greek money. Any bank account will have to immediately be translated into local currency. Also, no one will be allowed to move cash Euro between the member countries. 

One way to immediately establish the new currency would be to simply stamp the old money with country specific stamps.

Citation

Note that Greek's new finance minister implied that their train of thoughts follows exactly these lines of thinking [my own translation]:


  Greece is not going to leave the currency union, as it cannot go back
  to the path of development on which it was on, hadn't it joined the
  union. An exit would lead to chaos in any case: For the moment, there
  is no new Greek currency as a new Drachm. Preparations for the
  introduction of such a currency would take months and would have the
  same effect as announcing a depreciation several months in advance.
  But you can only have a depreciation over night and unexpectedly,
  otherwise there are massive movements of capital flight/export.


From this german article:


  Die Währungsunion verlassen soll Griechenland nach den Worten von
  Varoufakis aber in keinem Fall. Denn damit könne das Land nicht auf
  den Entwicklungspfad zurückkehren, den es ohne Eintritt in den
  Euroraum genommen hätte. Ein Austritt habe auf jeden Fall Chaos zur
  Folge. Denn gegenwärtig gebe es keine griechische Währung wie eine
  neue Drachme. Vorbereitungen für die Einführung einer solchen Währung
  würden Monate dauern und hätten die gleiche Wirkung wie die
  Ankündigung einer Abwertung mehrere Monate im Voraus. Doch eine
  Abwertung könne es immer nur über Nacht und unerwartet geben, sonst
  gebe es riesige Bewegungen zum Kapitalexport, warnt er.