First, you must unlock whips by completing all qualify tracks in Germany Career zone.
Once you have unlocked whips simply swipe your finger from the throttle over to the right while in the air. Return your finger to throttle before landing to complete the whip. You can control the size and speed of the whip by how far and fast you swipe.
If you use auto throttle the technique is the same but you need to start your swipe from the whip button instead of the throttle button.