Place newly purchased hat on head. Note the high, sloping forehead, the flattened brow/brim. You look like a Neanderthal. Using scissors, remove the fibrous underbelly found inside the front of the cap. Congratu- lations... you've entered the Tool Age.
Take a shower with your cap. Not only will the moisture shrink the hat to fit your head, it will prepare its brim for the next step. Using an herbal shampoo, gently massage your hat. Rinse and repeat.
For this step,
you'll need a friend. While you curl the brim slightly with your weaker hand, have your friend place one baseball into the base of the brim and a tennis ball near the edge. Secure them with rubber bands This will provide the perfect "cone-shaped" curve you desire. Be careful! Others may be distrustful, even frightened, of the perfect symmetry that graces your crown.
Ideally, your cap should be worn low enough on the head so that you can monitor its shape at all times. Should you perceive any distortions, remove the cap immediately and place the brim on your knee. Perform any necessary adjustments by hand, using your knee to measure your progress.