I'm a right-handed player who putts with my left hand. I tried a hundred different putting styles, but this one works better for me than any of them. Without my right hand on the club I'm able to stand taller, which affords a better view of the intended line. I also don't have to worry about twitches, staggers, jitters and jerks ("yips") of the right hand taking my club face off-line.
I use a John Riley Tri-Liner:
The ball is just to the left of my right foot, and the club face is just to the right; my right foot is pulled way back.
The COMPLETELY relaxed left arm hangs virtually STRAIGHT DOWN, with absolutely NO leftward, rightward, backward, or forward push or pull on the shaft, and zero torque (twisting action) employed to keep the face square. If these conditions are not met, then forget it. Move your head one way or the other, or shift your stance slightly, if necessary, until the club in your completely relaxed hand and arm hangs straight down, achieving this without the use of any force except the supporting upward pull by your left hand, and the competing downward pull of gravity.
The thumb must be on top of the shaft, else if the thumb is a little on the right side there might be a tendency to push the shaft on the way down. That must not happen: the motion down should be purely pendulum-like in nature.
Naturally, the center line of the Tri-Liner points at the center of the ball, and the face is square to the intended line; the club is about 1/8 of an inch off the green.
Take the club back however far is necessary in order to achieve the desired distance. The arm and shaft remain on the same line going back, and there is no breaking of the wrists.
Now, here is the BEST part: don't worry if during the takeaway the face angle changes; your backswing won't be perfect; let the face angle change if it wants to; do NOT attempt to fix the angle going back, or coming down. On the way down, let gravity alone pull the club down to impact. If your arm happened to twist a little going back, it will automatically twist back into proper alignment in time for impact. Keep your arm and wrist TOTALLY relaxed, and trust that the club face will return to its exact position at setup. Do NOT attempt to manipulate the club's face angle on the way down. If your arm and wrists are totally relaxed on the backswing and downswing just as they were at setup, the face almost magically finds its way back to a perfectly square position at impact. If your face was square at setup with relaxed arm and wrist, is is guaranteed to return to the same place. Do NOT pull the club down to impact; if you leave that job up to gravity, you won't be disappointed. The motion down should be pendulum motion only. Just let it all happen.
The key is trusting that gravity alone will get the job done, and trusting that it is not necessary to worry about minor club face angle changes during the backswing. If you make any effort at all to adjust the face angle, you will fail to return square to the ball. Likewise, if you attempt to intervene in the natural gravitational course of events on the way down, your club face will fail to return square to the ball. If the face was square at setup and the club was hanging vertically, freely, at the end of totally relaxed arm and hand, it will return to square through gravity alone, as long as you do not manipulate the face angle on the way back, or the way down. You will be AMAZED at how well this works.
Some PGA pros have done well putting with one hand; Mike Hulbert is one example, but he was a right-hand player putting with his right hand. I am a right handed player putting with my left hand.