Look for patterns in your subject matter, no matter if they happen to be natural or artificial. Patterns add an appealing aspect to a photograph, particularly if they are repeating patterns. You can play off these patterns to get unusual angles or frame your subject relative to the background.
In life, people are trained to always create things that are almost perfectly even. While symmetry and perfection are things people look for, try and take pictures of your subject off center. Beware of auto-focus features that lock in to whatever is in the center of the lens. Use manual focus instead, and lock your focus before snapping the picture.
Allversity Photography Course: Composition.