Ok guys so I'm just going add my opinion on how to hit a buggy whip running forehand for a righty step by step:
1. Obviously, split step then go into the unit turn.
2. Start running towards the ball with your shoulders turned. It is important to keep your non hitting hand on the racquet for stability. You do not want your racquet arm to be bobbing all over while moving to the ball.
3. When you feel like your close enough to the ball, use you left hand to release the racquet are start your swing.
4. Now this is the key step where I see a lot of differences in explanation by posters. You want to do these three things almost simultaneously: a. Contact the ball with your swing b. Do a cross step(its actually more like a hop) with your LEFT leg, when you land all your weight is going to be transferred on the left, while this happens you... c. KICK your RIGHT leg upward.
5. With the kicking motion of the right leg, you can then bring that leg around, plant the right foot, and then push off with that right foot to recover.
This video is the perfect example I want to emphasize for steps 4 and 5. Watch Azarenka's feet, step 4 is basically one smooth motion. At 0:25 she takes her last step with her left foot, as she steps she kicks the back leg. At 0:32 starts step 5 where the right leg comes around and plants.
Here is another video of a running forehand. Pause at 0:22, notice how his right leg is kicked up and by 0:23 he is ready to push off with his right to go back in to the court.
Keep in mind that 4 and 5 happens basically in one step and the motion takes a lot of practice to get use to.
Sorry if my explanation might be a little complicated to understand. Please watch the youtube videos, it is exactly the type of technique I had in mind. I see many of the pros use this especially Nadal, Sharapova, Azarenka.