1. I think more about the speed than line on my putts. For example, when my caddie tells me inside right or inside left, I just putt to the center of the hole and make sure my speed is enough that the ball will reach the back of the cup. This takes most of the break out of the putt and simplifies the stroke. I putt aggressively, but not too aggressively so as to avoid a nasty lip out.
2. For all putts standing with my eyes over the ball I found to be critical. This simplifies things enormously and makes it easier to sink straight putts.