The hardest thing for the beginning golfer to learn is how to swing at the ball and hit it. Putting, on the other hand, seems to be so easy because you can't miss. Only when it comes down to getting the ball into the hole does the true nature of putting reveal itself. Here are a few ideas that will help.
It is true that you want to hold the putter lightly, but many beginners hold it too lightly. The goal is to hold the club only as firmly as is needed to make the putter move all as a unit. Another way of saying that is, the grip and the putter head must move in the same direction at all times.
When the putter is held too loosely, the club starts moving back, but the putter head doesn't move until a split second later. The grip end is moving to the right, but the putter head isn't. The same thing will likely occur when the putter is brought back into the ball. This "wobbling putter" makes it hard to hit the ball hard enough to get to the hole, and difficult to keep the ball on line.
Aiming is next. The ball will go where you aimed your putter, and that means the face of the putter is square to the line you want the ball to start rolling on. It takes more care to get this right than you might think.
First, draw that line on the ground in your mind's eye and set your toe tips parallel to it. Next, make sure you're standing directly over the ball. Hold the end of the putter up next to your left eye. It should point right at the ball. Finally, find a spot in the grass a few inches in front of the ball and along your intended line. Use that spot to help you square up your putter's face to that line.
You might think only about hitting the putt straight, but hitting the ball hard enough to get to the hole is even more important. If your line is off on a twenty-foot putt, you might finish a foot to one side of the hole or the other, but if your speed is off, you can easily finish five feet too short or too long.
Practice getting the speed right by first kneeling down and rolling balls at the hole with your hand. This will give you a feel for how much energy it takes to get the ball there. Try this from different distances, like five feet, ten feet, and twenty feet. When you're rolling the balls close, start hitting them with the putter, borrowing from the feeling of rolling them by hand.
If you get these three fundamentals down, you'll be a good putter right away.