Once you have yourself a reliable stroke that works...
1st....make 100% sure your aim is perfect on every putt....pick a little spot on the green 6 inches in front or w/e....roll the ball over it.
2nd....try using a Clear Key over the putt....w/e it is....some song in your head or w/e....it'll keep your conscious thoughts at bay while you're hitting the putt. Stick with it for a while if you're gonna give it a shot....it takes a bit for your "system" to get used to it so it works to it's full effectiveness.
Taking it to the course revolves around The Computer. Read the putt without omitting any of the slightest details. Visualize that which you want to happen. Press the "you" button and let it go.
Taking it to the course requires proper "mechanical practice" and proper "playing." Perpetuating the thought of putting being simple only makes it more mysterious and complex.
Practice with Purpose. Play with aid from the Computer and by feel.