The key to being able to deal with long distance putts effectively is to have really good distance control with your putter. The best long distance putters are all able to putt the ball really close to the hole, to within a few feet of it, with just one putt.
This will now leave a very short, makeable putt and as a result they take far fewer putts on the greens, meaning they shoot a much lower score.
Being able to lag a putt well, that is being able to roll it up to within a few feet of the hole, will ensure that you take two putts maximum when putting from distance. Reducing and even eliminating any three putts from your round will massively influence your score and help you to reduce it.
Lag putting, getting the ball close from distance, is something that you can practice, improve and become much more skilled at. Direction does play a part in lag putting, but by far the more influential element is distance control. Even if you just generally aiming the putter face in the direction of the hole, you will never be too far out left or right. However, if your distance control is not accurate you can easily leave the putt 6 or more feet short, or long and this will now mean that you face a very difficult second putt.
To work on improving your distance control, try incorporating the following drills into your practice schedule.
With the first drill, stand on one side of the putting green. Position yourself so that you have a long putt across the green to the far side. Play putts to the far side edge of the green and work on getting the ball to finish as close to the edge of the green as possible. Count how many goes it takes you until you have the ball within three feet of the far edge. Now putt to another side. Make sure you still have a long putt, but a different distance to the previous one.
Play putts at the new position on the far edge again, until you have the ball within three feet. Work on achieving this in less putts than it took you before. Keep repeating this drill, changing putt length and your position after you have successfully got the putt to within three feet and keep working on completing the task in a lower number of attempts, until eventually you can make the putt in just one go.
As an alternative drill, take two tee pegs and place them on the green approximately eight feet apart. Set yourself up on the green so that you are putting directly in line with both tee pegs on your putt line. Ensure that you are the distance away from the first tee peg that you would class as a long putt. Now play a putt so that it finishes between the two tee pegs. It does not need to finish directly in line with the tee pegs. You need to work on the distance control and get the ball finishing distance wise no further than the far tee peg and no closer than the near tee peg. You score a point if you get the ball in this position. To score your next point, you cannot hit this putt past the ball that just scored but it must go past the closest tee peg. If the ball finishes in that position you score, if not the game is over.
Keep playing until you do not score and work on achieving as many points as you can. This is a really challenging game to work on, it certainly is not easy, but with practice at this and as your score improves through playing it, your distance control will improve and you will find long putts much easier to handle.