There are many different levels of formality in America. In clothing there are three broad groupings: casual, business, and formal. Each of those have their own subdivisions. The level this relates to is the formal level.
If you are going to a wedding you are expected to look your best. Sometimes this means adding just a few minor touches. One such touch is the pocket handkerchief.
Step 1: __init__
The first step is to make the base. It is actually a shape used very commonly in origami and paper plane making.
Bring all four courners together and make sure all four sides bulge out. Take two adjacent bulging sides and pull them tight and give it a shake. This is the base shape.
Step 2: Easy Isn't It?
Fold down three quarters of the front corner.
Step 3: WEll, It's Not Hard at Least
Fold the bottom 3/8 up. Try to bring the point exactly along the center line.
Step 4: Second Most Difficult Step
Fold the sides in equally to the width of your pocket.
Step 5: The Hardest Step
Shove the folded kerchief into your pocket. The most difficult part is not twisting it or making it uneven. Take a moment to adjust it, and your done. You now look 8.7% fancier. Good job.