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.
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.
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.
Note that Greek's new finance minister implied that their train of thoughts follows exactly these lines of thinking [my own translation]:
People have argued that if the rich countries (sometimes just Germany) left the Euro the resulting dislocations would be much smaller:
But are there any modern examples of currency unions breaking up in an orderly manner with minimal economic disruption? I can think of some currency pegs that ended without major harm but I can't think of any actual unions that ended without doing so. The rubble union dissolving might not have been a huge deal but only because the other changes to the affected countries were enormous. Maybe the dissolution of the Scandinavian Monetary Union in 1914 would qualify but WWI loomed large in that decision. War, financial crises, and depression do see to be the most frequent fellow travelers with dissolution of currency unions. Perhaps that's not because dissolution is horrendous so much as it is a high risk, relatively low reward strategy that is only worth trying when things are already terrible.