Having the “touch” in your mind’s eye to know how firmly to stroke a putt (so its speed matches the break) and then also having the “feel” in your body to execute that touch is gained only through experience and solid practice. See No. 1.
Each picture—taken shortly after impact with a driver (left) pitching wedge (middle) and putter (right)—shows that my right hand is in almost the same position just after the strike: a little “on top” of the shaft and in-line with the target line.
If you execute about a dozen of these escape swings on the range every time you practice you’ll quickly learn how punch shots typically react after impact. It’s critical to know—and be able to control—how far these shots fly and roll out. There’s nothing worse than hitting an escape shot “perfectly” only to see it carry too far or roll into even greater trouble.