Composing a compelling photo can be a challenging artistic endeavor; after all, what looks great in real life can be flat and uninspired when captured as a photo. It's not enough just to capture what you see with your eyes; you need to reinterpret the scene for the medium that we used to call film.
Thankfully, photographers have had almost two centuries to codify successful compositional techniques into a set of rules. You almost certainly know the most common rule of composition, the Rule of Thirds: Divide what you see in the viewfinder into thirds, like a tic-tac-toe board, and arrange your subject at one of the intersection points. And most cameras--including the iPhone--let you turn on a grid or guide lines to make the scene easier to frame.
Many other rules of composition are less well known, but they're easy to apply and will add a lot of variety to your photos. Here are the top five to try out in your own photos for whatever camera you use.
Framing: Wander through an art gallery or museum, and you'll see that artists have traditionally liked to surround their images with fairly ornate frames. Even though frames have gotten simpler in modern times, framing is still important--it helps set the subject off from the physical world. It sets boundaries. And that same technique is actually quite powerful within the photo itself. Study photos with a critical eye, and you'll find that pros use many elements in their work as natural frames to surround and isolate the key subject in a scene.
Leading lines: Photographers and magicians have a lot in common; they both are masters at making you look where they want you to. Photographers do this with leading lines, which are elements in a photo that lead, or pull, your eyes through the photo in a specific way. Imagine a road, a river, a line of ducks, or any other "line" that moves through the scene. Leading lines can be straight or curved--what you include in the photo and how you arrange it is up to you.
Symmetry: The human brain is attracted to symmetry. In fact, psychologists say that a key component of physical attractiveness is how symmetrical a person's face is. You can incorporate symmetry into your photography by composing a scene in which the same visual elements appear on both sides of the photo.
Asymmetry: Then again, every rule is made to be broken, and some asymmetry actually makes for a much stronger photo than perfect symmetry. In particular, look for scenes that are, in fact, fairly symmetric, but where one element is unique or out of place. This asymmetry creates tension and acts like a magnet to draw the eye--much like the leading lines mentioned earlier.
Depth: Modern 3D photos and Lytro images notwithstanding, photography is inherently a two-dimensional medium--your photos are flat representations of the 3D world. Perhaps that's what is so compelling about the concept of depth. When done right, photos can effectively simulate depth and lead the eye from the front to the rear of an image.