Speaking of the "technical means" some have mentioned, a man with whom I work takes finely composed photos. The interesting thing is that he came from film and then with a DSLR, only rarely uses manual. The "beep" is set to indicate focus, which is ok but rarely does he manual focus. To get a good pic he goes from setting, meaning the auto settings on his camera, from landscape to portrait, to night scene, those sorts of settings I never use and my D200 does not have such settings, just ISO, White Balance and  Quality.

A man I knows is both a gemstone dealer and an editor for a leading fly fishing magazine. He has the expensive gear. What does he use for macros for the net of gemstones? His Sony digital, point and shoot with manual over rides.  What does he carry into a trout stream after a hike to the place, the same Sony.  The  SLR and DSLR are just too much for a lug up the trail and in the middle of a brook when trying to catch trout and get a picture. He told me the macros are better than from his very expensive SLR macro lens...

My main point is that some folks do have an eye for what is pleasing and artistic.  Some must learn to duplicate as best they can with a similar process, even if not an easy natural move for them.

For those whom are are given as a sort of natural blessing an eye for things pleasing and artistic, that is the raw talent I mentioned. Sure, the technical must be mastered enough to take that talent and produce a decent image.  Sure, others without a natural eye for the composition can learn the means to see these images, even if not at first from the spirit of it all but see it nonetheless.  Practice, practice, practice.