Look in the bottom right corner of your screen. You'll see the names of everyone in your party with a quickening. If one of those names appears in white hit the button that appears next to it. That chains them to the quickening being performed. Once they start, then the names will reappear. Find another name in white and hit it. If there are no names in white then hit R2 to reshuffle the names and hopefully get one in white.

Since Ashe was my first I thought I was supposed to hit R2 to shuffle the spots light come out of below the enemy to do better damage. It wasn't until I had multiple characters get a quickening that I realized what was up.