Missing greens isn’t all bad. It depends on where you miss them. You can often get back in the hole with your basic pitch or chip. It’s the tough lies to watch out for the ones that test your finesse and precision.
That stat which comes from putting studies I’ve done using PGA Tour ShotLink data should scare you. Say you face 12 putts of 30 or more feet per round (which is about right for a mid-handicapper).
Plan for zero spin and 15 feet of roll once the ball hits the green. It may not get you close enough for a one-putt but it can definitely save you a stroke from a spot that normally leads to blowups.
As you start the club down keep your left arm straight so that your swing bottoms out under the ball. Let the club “kiss” the grass. No need to carve a huge divot. Don’t “hit” the ball. Accelerate smoothly through impact. Your goal: Reach max speed about four inches ahead of the ball.
That’s all there is to it! I find it helpful to swap fearful thoughts (It would be awful to chunk this) for finesse ones (Just “kiss” the grass). Embrace the moment and be smooth. Oh and your lower body should work just as hard as your upper (weekend players tend to “deaden” their legs around the green).