It's really hard to learn these things when they don't come naturally, and even for those of us that it does we still have to take time out to practice and shake it up. I don't know if you have a particular genre of photography you focus on, but I largely shoot nature, and quite often the setting and subject chooses my composition for me. When I want to stretch my artistic legs and tackle a concept to get better at it, I pick a fairly mundane object and I spend an hour or so photographing it in as many which ways as I can to accomplish the task at hand, be it composition, lighting, posing, whatever. I base all of this off of a painting assignment I had in my Painting II course in college. We had to pick an object (mine was a nifty swan soap dish) and every painting we did that semester (upwards of 20) had to incorporate that object somehow. We used it to study color, composition, pattern, texture, a whole load of things. I learned more from that swan in that semester than from my previous three semesters of painting, and I continue the project to this day with photography.