Draw the Line
First thing you can do to help your putting is draw a straight line around the equator of your ball (Picture 1). It's perfectly legal and really does help ensure you align the putterhead exactly as you want (Picture 1.). To be honest, I'm not sure why you wouldn't do this (at least give it a try) as it's so easy to do and very effective. It's obviously far better a visual aid than the word 'Titleist' or a Nike Swoosh (and better I think than the smaller lines some companies are now putting on their golf balls), and also gives you good feedback on the quality of your strike. If the line remains straight, you obviously struck the ball flush with a square face. If it goes awry, it's likely the face of your putter was slightly open or closed at impact and you gave the ball a glancing blow.
Where you choose to position the ball when putting is a matter of preference, but I'll give you two truths that might help you decide where you want it. First, I have never seen anyone putt with the ball nearer their back foot than their front, and second I've long advised students to favor the instep of their front foot rather than somewhere towards the middle of their stance. I have seen plenty of good putters who position the ball roughly midway between their feet, but far more often than not, better putters have it significantly further forward (Picture 2). Don't let it go as far as your toes as that will breed inconsistent roll. Somewhere between your front instep and a spot an inch or so ahead of center will work best. Experiment to find the optimum place for you.
Eyes on the Line
A lot of teachers will instruct you to position your dominant eye directly over the ball. That works certainly but I would say as long as the eyes are directly above the line of the putt (Picture 3) - either directly over the ball or a little behind it, which was how Jack Nicklaus putted - then you'll do fine. Again, experiment a little to see where you make the best contact with the ball and achieve the most consistent roll. The majority of the best putters I know position their eyes over the line, although I have seen many competent putters place their eyes inside the line. However, no good putter I know has ever putted with the ball nearer to his toes than the point directly beneath his eyes.
Maintain Your Set-Up Posture
Okay, it looks like the ball will miss left (Picture 4) but I assure you it caught the left edge and dropped. But that's not the point of the photo which is to demonstrate how I maintain my posture until long after the ball has left the putterface. The only parts of my body that are moving are my hands, arms, shoulders and head which I allow to swivel slightly just so I can see the ball go into the hole. My spine is still tilted at the angle it took at address and my hips, knees and feet are static.
Nicklaus once said that while you may never be able to hit the ball like he did, there was no reason why, with a lot of practice, you couldn't putt as well. He was right (as he usually was about anything to do with playing golf); putting is not a terribly athletic discipline. It involves moving a putterhead back a few inches and stroking it through a few more. How effectively you move that putterhead depends largely on how you set up to the ball. Follow my tips above, practice the positions until they are natural, and I am sure you will develop a more consistent stroke as a result, and ultimately hole more putts.