I am not sure if this is entirely correct but this is how I was taught to fold a Tricolour in the Catholic Boy Scouts of Ireland.

  1. Fold the orange section over on top of the white section.
  2. Turn the flag over and fold the green section over similarly on top of the opposite side of the white section.
  3. Fold the flag in half doubling the orange section in on top of itself, leaving the green on both sides of the remaining square.

The idea behind this specific folding pattern is so that the orange and green sections symbolically never touch. The orange section represents Protestant settlers in Ireland (there is a William of Orange connection but I am unsure as to what) and the green section represents the Catholic indigenous. Because of the conflict between the two in the past in the Republic , the white is included in the flag to represent peace, and to separate them when the flag is folded. Presumably the green section is left foremost as it is the National Colour of Ireland. I have seen the flag folded triangularly รก la The Stars and Stripes, to my knowledge this is incorrect.