There are many ways to fold a pocket square; pick the one that suits your personality best.
Hold the pocket square from the center, letting the points hang down.
Pinch off the square in the middle.
Tuck the points up inside the square. Place in the breast pocket.
Puff and arrange as desired.
The Pointed Puff
Follow steps 1-2 above for folding The Puff, then add:
Flip the points upward instead of inverting them.
Place in the breast pocket and arrange as desired.
The Folded Puff
Hold the pocket square diagonally. Fold the top point down.
Hold both sides at the folded edge.
Bring the corner points in towards the center.
Fold the bottom half up and back.
Tuck into the breast pocket.
The Winged Puff
Hold the pocket square from the center, creating a puff with the points facing down.
Pull up any two points, making them level with the top of the puff.
Gather the remaining material at the bottom and fold under.
Tuck into the pocket and arrange as desired.