You can't control the big 3 - so you are quite limited. However - you can control your composition - at least most of it.
Never shoot something so that its directly in the middle of your picture. The Rule of Thirds is a biggie in photography. It means you should place interesting objects, or your subject at one of 4 intersections.
take a sheet of paper and draw 2 vertical and 2 horizontal lines - trisecting that sheet. You want the lines equidistant at 1/3 the page each. You end up splitting the paper into 9 "zones". Now look and see where you have intersections. There will be 4. In your mind - split up your viewfinder (does that cam even HAVE a viewfinder???) Place your subject at an instersection Try with something else and place your subject at one point and another item at another intersection.
Learn to "see" -
Take an ordinary object - could be anything, a pencil, a fire hydrant, a key, a shoe, a used bandaid - and photograph it from every conceivable angle. Place your object in different light. Take different angle shots, try upside down. Early in the morning - midday sun, while raining, etc.
This exercise helps you see an object and pay more attention to it.
Angles - In a photograph everything is angles. Your viewpoint can significantly alter your picture. Take the same picture standing up, and again lying prone on the ground. Take a picture of your front door while laying on your back with your head against it. Try to focus on the knob. This is quite an interesting exercise - its meant to open your mind up and let you discover that every scene is relative to how you see it (your viewpoint).
I always take pictures of stuff that is repeating (like a picket fence), or converging, like railroad tracks. I like weird angles and finding patterns in things.
Hope this helps.