Golfers may 3-putt for several reasons, but the top two stand out:
1) Poor Green Reading
2) Poor Speed Control
The first, poor green reading, is the number one cause of 3-putting that I see. If you think the putt is uphill right-to-left, and it’s actually downhill left-to-right, you haven’t got a chance. Poor green reading directly affects the player’s ability to control speed, too, hence it’s number one on the list.
I recommend players first learn the principals of reading a green: Being able to judge Slope Direction and Slope Amount. To practice, start reading greens by walking around the hole in a circle (a la Tiger). Visually check with your eyes to discover which way the putt may break; then use your feet to confirm what you see. See if you can feel one foot lower than the other, and how much weight is on each foot when standing near your line. Both your eyes and feet can also help dial in how much uphill or downhill slope the player must navigate, too. Practicing green reading on the practice putting green is something I never see done by amateurs- yet they wonder why they struggle on the course!
Second, poor speed control (touch) with the putter is the most common stroke issue I see with players who often 3-putt. While seeing a professional coach is best, a quick strategy is to check that your back-swing and thru-swing are roughly similar in size. Check that as you hit longer putts, your stroke gets bigger in size, too. One of the most common flaws is to have too short a stroke with long putts, and too long of a stroke with short putts. This leads to poor speed control, leaving the player with too long of a second putt after their lag attempt.
Improving both green reading and speed control with the putter are the first two places to start for anyone struggling with 3-putts (or even 4-putts!). Good luck!