Hitting out of deep rough with the wrong game plan can be a round disaster for many amateur golfers. I think the most important decision to make is pre shot and determining the best place to miss the shot to make par. Often that could mean taking one less club then the normal yardage and try to get the ball on the front of the green or an opening in the approach. After the pre shot decision is made, I try to get the golfers to swing the club steeper on the backswing then normal (visualize the steep high hands of Justin Thomas), and steep on the downswing through the hitting area and try to keep the toe of the club from closing quickly at impact.
I have also found it easier for some amateur golfers to set up with the club in an open position and then make their normal swing. The club will naturally close out of the high rough.
Different golfers can find success in different ways and it is important to try as many methods as possible, see what works best for you. Regardless of the method, the goal should be to make par as easily as possible and that rarely means trying to pull off the ‘hero shot’ out of high rough.