Putting is one of the hardest things to do in golf. The main thing to do is to keep your eyes on the ball. Your eyes need to be right directly over the ball, so the way you stand is truly up to you, but your stance and posture will change according to the way you can actually have your eyes directly above the ball.
Look at the hole very closely from where you are standing. Decide where you want your golf ball to go in. If the break is left to right then you need to enter the hole on the left side. If it is from right to left then you will want to enter the hole on the right side. In the majority of cases, golfers use the face of a clock and want to enter at the 7:00 view. The hard part is often the speed of the ball as it can go right past the ball, so practice on the green putting is very important.
Some golfers will move their left hand a bit lower and just a bit toward the hole as they make the hit or stroke. You still need to ensure that you are keeping your posture correct and your shoulders in a level position. All bending should be from the hips down if needed.
The best way to practice putting is to go to a putting green and only use one hand so you can get the feel of the club. Most golfers spend more time on the putting greens practicing than another area of the course due to putting being very important and all greens are completely different. Some are sloped from one side to the next and then go straight to the hole. No matter how you decide to practice putting even at home with a cup, remember out on the green the slopes and creation of the greens are not going to make it easy for you to putt your ball right in, no matter where you may be on the green.