Try not to be aggressive with your steering otherwise you will skid out.
In order to initiate a drift, get some good speed up then just as you start turning into the corner tap the (PS) / (Xbox) button then feather the either left or right to keep the drift going. The Subaru Impreza WRX STI is a car found in the Sports Series so load up an event that accommodates this series such as the Title Fight Duel in the Big Timber Forest area, ensure you choose the Suabru Impreza WRX STI then start the event ensuring you drift as much as possible