As we all know, the quickest way to lower your score on the golf course, is to practice the short game. Yet many golfers prefer to hit golf balls at the practice facility or play 9-holes rather than practice putting. When practicing, remember putting is all about distance control - so it's more important to get comfortable with this, before worrying about which way a putt will break.
To begin on the practice green, roll golf balls to different holes with your hand rather than with a putter. This will help you get an idea of the speed of the green.
Once you have a feel for roll and speed, you can work on reading greens. This begins as you walk toward the green. Look for big slopes and pick a place where you want the ball to finish (hopefully near the hole.) Again, roll a ball toward a hole and see if it does what you thought it would. Now hit the putt and watch the ball to learn what it does. Reading greens is based on practice and experience - so take 30-minutes each week during your golf season to practice putting.
Some good drills include practicing from one putter-length from the hole (probably a 3' putt since most putters are 34"-36" long.) See if you can make 10 putts in a row from this length. Once you master 8 or 9 out of 10 putts, move to two putter-lengths and try to make 7 or 8 out of 10. If you miss a putt, go back to one putter-length and try for 10 again. This builds confidence in your putting and is much more productive that standing at one side of the practice green and hitting giant lag putts at holes from 30' away.
When you transition to the golf course greens, your goal is to have two putts or less, so make sure you give the first putt a chance to make it close to the hole so you have an easy second putt. Practicing speed and distance control will help you achieve that goal.