Have you had a chance to play a round and record your putts alongside your score? It's a really useful exercise because it helps you concentrate when putting. It also helps you analyse how you got to the green. My putting is improving but I am not reaching the green in regulation often enough (yet!)
I recently googled "Putting tips and drills" and found about 5,670,000 results (0.44 seconds.) Clearly a subject of great importance. I haven't got enough time left in my life to read that much so I try and keep it simple for myself. I assume a comfortable stance and a natural grip that suits me (...how many different grips are there among pro golfers let alone the rest of us?) I focus on keeping my head dead still and my upper body steady or quiet. You need to avoid lateral sway and "bobbing." I focus on the ball through the back swing and forward stroke and I make sure I witness the putter face striking the ball. Additionally and most importantly I try and focus on where the ball WAS, resisting the urge to look up. Looking up prematurely can affect the strike and follow through causing mishits. On short putts, try to hear your putts drop, don't see them. This helps with longer putts too.
A leading, Hall Of Fame Golf teacher suggests putting a five cent piece under the ball when putting, making sure that you focus on the ball until impact and then on the coin after impact. This is a helpful drill.
My training aid ACUSTRIKER, will help you keep a steady upper body, a still head and encourages you to witness impact. The round black "Putting disc" will help you perform the drill mentioned above.
On a final note... don't be afraid to use your putter from off the green and on the fringes. It eliminates the risk of a chunked or skulled chip and can get you close to the hole.
Jack Nicklaus “I’ve said before that if you can putt the ball from off the green, it’s the best way to get the ball close to the hole.” ( a tip given to him by Arnold Palmer) Your worst putt is often better than your best chip.