(1.) Keep a steady head. Do not move it even a millimeter. I notice that when I keep my head dead still - I putt my best. Especially on long - lag putts... A steady head is crucial.
(2.) Pick something to stare at - on your intended line - and lock into it - really focus and be deliberate - in your focus.
a.) You should be able to get to a point where nothing else is in your head except for making the putt - and hitting that line / spot / dot.
b.) As Dave Stockton states... The mental aspect to putting is critical to becoming a successful putter.
c.) You have to be confident. Almost cocky with your putter IMO.
d.) Do not second guess yourself.
e.) Be positive - even if you miss or 3-putt a hole.
(3.) Alignment is key. Get the proper alignment aids (ball, putter) to eliminate the guessing if you are really lined up appropriately or not.
a.) I picked up the TaylorMade Spider Ghost because it has one of the best alignment systems for my eye - it is so easy to setup.
b.) I use the GoPro alignment tool to get a nice line drawn onto my ball - it helps me line up my putts and takes guess work out of ensuring the ball is on a proper center line with my putter
Seriously though, if you are having issues with breaking 36 putts in a round... It has to be a mental mind block IMO. But to ensure you have the proper stroke that becomes second nature like signing your signature on a piece of paper (read Dave Stockton's book Unconciuos Putting)... Get a Putting Alley http://puttingalley.com/. And practice just making putts on it for 15mins a day. I guarantee that it will improve your make % from 1, 2, 3, 4ft... Even 6ft. In fact, I'd say my make % from inside 10ft is significantly better than it was a year ago after making some subtle changes to my equipment and practice routine. The great thing about the Putting Alley is it is so easy to setup and use anywhere at your home or office. And it will ingrain a solid stroke so that you increase your makes - and the putting stroke becomes second nature.
For instance, over my last 20 rounds... I'm 1.7 putts per hole and 1.9 putts per green in regulation (GIR). That's not too shabby... I've had less than ten 3-putts over my last 20 rounds. And only one round where I had more than one 3-putt within the 18-hole round. I'm not perfect with my putter... I still have a some room for improvement... But my point here is that if I can get down to 30.6 putts per round average... Then you can too.