There are many different styles of folds. Try for a casual not too studied look for your pocket square:
Four Point --with the pocket square on a flat surface, pick up each of the four ends and fold over leaving the points or ends higher than the middle. Place in pocket so that the points show.
Puff – Pick up the square in the center with the four points hanging down, fold over and insert in your pocket so that just the "puff" is showing and spread it to fill the pocket opening.
Three Point -- fold the square into a perfect triangle with the flat side toward you, move the lower left corner to the right of the triangle then move the lower right corner to the left of the top point, adjust the three points so they are even, fold the bottom up less than half way and push into your pocket.
TV Fold – very 1940-50’s! Fold the pocket square to 1/8th its full size, insert into pocket with ˝ to 1 inch of razor straight square showing above the pocket.
Peaks – Start with the square open, fold over diagonally to form a perfect triangle with the flat side to your right. Fold the bottom edge up to the right of edge farthest from you and a little higher, move the left edge slightly higher and to the right of the two peaks you’ve created and you should have three peaks or triangles. Fold the square and insert so that the peaks will show out of the pocket
Puff and Point -- pick up the four corners of the square, fold in half and put in your pocket exposing both the points and the puff center.