This fold works well with pocket squares that are multi-colored, since both halves of the pocket square will be seen in the different layers.
This one, "The Tail of the Phoenix" features a dynamic design with contrasting colors which will cause the triangles to stand out from each other.
Step 1: Fold the pocket square in half diagonally.
Step 2: Fold the left side over the right side, corner to corner.
Step 3: This would be a good point to iron the pocket square, to keep the edges crisp.
Step 4: Fold the top point down over the bottom right point.
Step 5: Rotate the pocket square so the border is on the bottom edge. Separate the points a bit so a little bit of each triangle layer shows on the top edge. Then fold the top point down toward the bottom edge, either forward over the front, or backward over the reverse side - try both to see which produces the nicer effect.
Adjust the top edges of each layer once you fold it over to show them to best effect.
Step 6: Fold the corners back behind the pocket square to reduce the width of the base so it will fit in the pocket. You can iron them in place or just hold them in place until it is in the suit pocket.
Step 7: Insert the pocket square into the pocket, and adjust the layers to show as much or as little as you want.
Here you can see the different appearance of folding the last corner over the front vs. over the back side of the pocket square.