An easy way to fold a pocket handkerchief is to lay it flat and fold it once to create a rectangle. Next, fold the rectangle so that the short edges are just short of each other, and then fold it in thirds to tuck into the pocket.
A common fold for the pocket handkerchief is the pocket square. Start by folding the handkerchief twice to form a smaller square. Match the far points together to form a triangle. Fold the remaining points in, and tuck the pointed end into the jacket pocket. This leaves only the straight edge showing.
A variation on the pocket square is the one-point fold. Start the same way to form the smaller square and then the triangle. Fold the remaining points in tightly to form a base. Tuck the handkerchief base down into the pocket so the pointed end is showing.
The two-point fold is another variation. For this style, make the smaller square again. However, this time match the far points, and then shift them so they slightly overlap. Tuck the remaining points in, and place the handkerchief into the pocket with the two points showing.
The puff fold is simple but different. For this style, lay the handkerchief flat, and pinch the middle. Use this pinch to draw the handkerchief up. Gather the bottom, and tuck it into the suit pocket, adjusting for shape as needed.