Putter alignment is absolutely crucial if you are going to improve your accuracy and take fewer shots once on the green.
To be able to stroke the ball along the target line, you must have the putter aligned correctly to the target line. If the face is aiming to the right of your target line, the ball will travel right and vice versa if you have the face aligned to the left. It is crucial to align the putter correctly at the target line if you are going to make the putt.
One of the main causes for aligning incorrectly is not reading the green, or reading the green but not doing this correctly. If you are not aware of where the target line that you need to hit the ball along actually is, you will not align the putter well.
To ensure that this is not the reason for mis-alignment, read the green before you line up. Crouch down directly behind the ball and directly in line with the ball and the hole. Look at the surface between the ball and the hole and notice the slopes that you are required to putt across in order to hole the putt. Once you have decided on how the slopes will affect the roll of the ball, you need to picture the line that the ball will roll along in order to finish in the hole. Look at this line and pick something out along it, about one foot or two in front of the ball but on the line to use to align the putter towards. You want to get the ball rolling correctly along the line of the putt and this is not necessarily directly towards the hole. Select a target on this line and use this to help you align the putter correctly.
If you read the green, can visualize the line that you want the ball to roll along and can select a target on this line to aim the putter at, then you may still align the putter badly if you do not have an alignment aid on the head to help you. You need to align the putter face at a right angle to the target line for it to be aligned correctly. If you struggle to see whether the face is at a right angle or not, then use a putter with an alignment aid/line on it. This is simply a line on the putter head positioned at a right angle with the face. Some putter heads have a smaller line than others and if you do struggle with this then select a putter head style that has the largest line possible, as the larger the line, the easier it will be for you to use. Once you have selected the target line and the mark to align to, work on making sure that the alignment line on the putter head is lined up to this mark.
If you find it hard to see a mark or spot on the target line, then rather than guessing where it is, use the logo on your golf ball, or a line drawn on it and aim this at the target line initially, as you can do this whilst you are still directly behind the ball, looking along the target line from the ball to the hole. Now you can align the putter head with the logo on the ball by ensuring that the line on the putter head is in line with the logo on the ball.