Android & iOS
Neither gamepads / controllers nor hardware keyboard are supported.
Windows
Both keyboard controls and gamepad are supported. You can find their button layout in the Garage - Profile - Controls Help.
However, you're free to use the gyroscope feature as an alternative way to control the car in Drift mode. Just tap on "Pause" icon in the upper left corner of the Suspension Test-Drive menu (Garage - My Cars - Upgrade - Suspension - Test Drive) and choose the "Gyroscope" steering option.