The twirl is performed from a slightly modified version of the standard drumstick grip. In order to get into the proper position, the index finger is moved around to the opposite side of the stick. This causes the stick to be between the index and middle fingers. The grip needs to be loose enough to allow for the stick to move through the arc. Gripping the stick too loosely causes it to fall out of the drummer's hands. It takes some time to develop the right feel to allow the drumstick to move properly without dropping it.
The twirl begins with the palm facing down with the drumstick between the index and middle fingers. Initially, the stick and hand are just rotating in this grip. Once the palm is facing upwards, the momentum of the stick needs to carry it through the remainder of the arc while the hand rotates in the opposite direction to return to the original position. Some very minor finger work is required to keep the movement of the hand from altering the twirl itself. Most of the twirl does come from the momentum of the drumstick, not from finger work.
Practice somewhat slowly at first until better finger control is developed. Practicing too slowly is too difficult, since the momentum of the stick is a contributing factor in the twirl. The goal is to move at a speed with the proper momentum to complete the twirl without trying to make the stick move as fast as possible.
The grip used in the twirl allows for enough control that the drumstick can be used without going back to the regular stick grip. Overly complex, fast drumming may be too difficult to combine with the twirl, but simpler parts with longer strike times allow for twirls placed between them with ease once a drummer is familiar with the twirl.