Summarize:

If you have an angular face with wide cheekbones, then you most likely have a diamond shaped face. Wearing a hat with a smaller brim and pinched crown like a fedora or trilby hat may be good options for you. An oblong face is longer than it is wide. Most people with oval faces also possess a round chin. Wear Fedoras with wider brims or western hats to pull attention off the length of your face. Avoid hats that have narrow brims. If your face is as long as it is broad then you have a round face. Try on asymmetrical hats because they create contrast with your symmetrical face. Hats with a high crown and peaked or a slanted brim look best on you. Avoid hats with tall rounded crowns or a rounded brim because it will bring attention to the roundness of your face. If you have wide cheekbones and a large jaw, then you probably have a square face. Wear larger floppy hats like the Derby hat, or choose a hat that has rounded curves and edges like a bowler. Wearing a hat with a prominent crown can make your head look longer.
Choose a hat with a smaller brim if you have a diamond shaped face. Wear hats with larger brims if you have an oblong face. Choose a pointed hat if you have a round face. Choose a hat that has curves if you have a square face.