Style is gained by landing various attacks on the enemy and lost when a character is struck by an attack. Style is also lost if a Character hits an enemy with the same attack three or more times in a row. This means that using the same attack repeatedly will drastically lower your Style and thus damage output, so it's important to mix up your attacks. While most attacks damage totals are affected by Style, not all are. For example, some attacks deal fixed damage and are entirely unaffected by Style.
Style can also be increased with the use of Items.