I'm by no means an expert putter, but with time and practice I have become much more proficient at it than I once was.
Assuming you've already read the FAQ's (over there --->) and searched-out for the many putting tips that have been shared here in the forums, I can only offer what I think has made the biggest difference (other than the Redwood Putter I use) in my putting ability:
"Feel".
I know it's an abstract term, so I'll attempt to clarify...
When you're out on the green (IRL), what do you do before your actual putt? Try to "translate" your normal address IRL to the putting in the game. Personally, translated for me, this results in me standing over the ball (in forward view), after pulling the flag to get a quick, unobstructed overview of the hole, and the course the putt must take.
After this brief "pre-planning" of the putt, I switch to reverse view. In this view, I take in the actual distance to the cup plus/minus the elevations along its length. Only after doing this do I consider the break(s), sometimes switching back and forth between views to "restart" the grid-dots so as to take note of their individual speeds. (This switching is only necessary on the longer putts where I sometimes find it necessary to "break down" the putt into segments for a better "look".)
Now, knowing the distance that the putt will have to travel, and having an idea of the break(s) involved, I begin the assessment of the actual power that I feel will be necessary to either "go against/with", or "go through" the break. This, I accomplish by visualizing the path the ball will roll towards the cup. I know... again with the abstractions... : / ... lol...
There are sooo many places around the cup that a putt can originate from... hence, there are that many different breaks that can occur along its path. I've learned not to fight those breaks, but to confidently work with them. Suffice to say that this "routine" I've developed for myself at address lends itself to not only lining-up these myriad of possible putting scenarios, but it also tends to relax me (my eyes/my reflexes) to the point where that particular putt becomes alot like all the others. The routine cuts away some of the variables that exist.
Isn't it apparent that some here at WGT can better "see" their putts? Low averages and high tourney placements, I believe, are built upon this ability to judge the greens. Not to say that the all-important approach shot is less a factor, but a quick look at the "more successful" among us will show that indeed, a well-trained putter has its place in lowering one's scores.
This "visualizing of the putt" isn't necessarily exclusive to those who've innately embraced its importance, though. I've developed my own - with practice - to the point where I can feel confident that, even though I may not drain it, I'll come awfully (and sometimes woefully... lol) close.
It's so much more than the "add this... subtract that" that some feel they should be capable of accomplishing in a game to "break it down to a science". Putting is not, whether it be in this game or IRL, and will never be a science. And I sincerely feel bad for those who miss out on the fun - the feel - of watching a putt drop into the cup, after setting it up and propelling it onto their chosen line.
Good Luck.