To TE Paul's last post, do this. Go through your pre-shot routine, and before striking the ball, be focussed on a specific dimple on the ball (if your eyesight is that good) or at a minimum, look at a specific letter in the brand name of the ball with which you are playing. After, and only after you have struck the ball, and can't remember what you were looking at, should you look up to see where the ball went. Good rule of thumb, on a 10 footer or less, you should only "hear" the ball go in the cup or at worst see it dropping in or just skirting the lip.
Next: On very fast greens with lots of slope, I think that spot putting is key. An over-read spot putt will likely have a slower pace at the hole and leave you more taps in (if you miss) than an under-read putt which will often times zoom by the hole and "never have a chance to go in" You will also leave yourself w/ more 3-6 foot comebackers.
As for drainage, everybody is right on with this comment. That is why, in qualifiers and other events, I always will go play in the rain on these courses I havent played often or maybe never even seen. That is the best damn way to get a feel for the slopes and breaks, PERIOD!
Finally, the consensus here is speed, speed, speed. I concur, that the right speed is everything. And to that point, let me offer you this VERY IMPORTANT TIP:
WHEN YOU START YOUR ROUND AND ARE ON #1 GREEN WITH A 18 FOOTER (or whatever length) MAKE SURE THAT YOU HIT THE BALL WITH ENOUGH SPEED TO GET PAST THE HOLE!!! YOU CAN ALWAYS ADJUST YOUR SPEED AS YOU GO BY BACKING OFF, BUT LEAVE THAT FIRST ONE SHORT, OR ON THE SECOND & THIRD GREENS YOU DO THE SAME.....WELL, YOU WILL BE BATTLING BEING SHORT ALL DAY LONG. DONT BE AFFRAID TO HAVE A FEW 3-6 FOOTERS EARLY, BECAUSE YOU'LL MAKE MORE PUTTS LATER. BESIDES, A PUTT LEFT SHORT NEVER HAS A CHANCE TO GO IN, BUT A PUTT WITH TOO MUCH SPEED ALMOST ALWAYS HAS A CHANCE...
Easier to back off your speed versus ramping up your pace.
Good luck!