One of the most important things that I believe each amateur astronomer should at least try is sketching. Sketching helps you train your eye. You have to sit and observe for a while. Often time we seem to get in a hurry just star hopping our way around only looking at an object for only a few moments. When was the last time you looked intently at an object for 10 minutes or more?? I'm guessing that most astronomers will honestly say that have never spend 10 whole minutes observing a single object.
Sketching forces you to spend time one objects. Once you begin to do it you will begin to notice more details, ones that you haven't seen before. It really is like adding inches of aperture to your telescope.
Astronomers long ago, before the age of cameras, used to study a single object all night and maybe many nights. Image what you could do if you did the same. Image how much greater our telescopes are compared to those used by the early astronomers.
I challenge you to go out and be an old school astronomer in today's world. Even when I'm not sketching I try to make it a point to always take a second look at what I'm observing.