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Go to the place shown in the video (open world). You can go there at any time. There is a safehouse / respawn point here. A car is parked in front of the respawn point. There's a high chance it's a "Berkley Gypsy". If you get a different car kill yourself and you'll get a new one (or drive away and come back later).
Drive the car up the road and then drift through the mud on the side of the road. To drift hold the brake and handbrake for a short moment and pull the left stick all the way to the left/right. You must drift for 5 seconds or longer in one go.

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