Rule of Thirds: Placing the main subject at one of the intersecting grid lines for the purpose that the eye of the viewer is automatically drawn there. 

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Balancing Elements: to create a more unique photo place your main subject off center as you would with the rule of thirds, also add an object to fill the rest of the space in the photo to create balance.

Leading Lines: think about how to place objects or choose your viewpoint based on the direction of lines because they can create a journey for the viewers eye.

Symmetry and Patterns: think about photographing scenes that have equal image on both sides. but introduce objects that create tension and throw off the viewers eye.

viewpoint: the place where you take the image from. rather than shooting from eye level you can get on the floor and point the camera up at your subject or get on something tall and shoot your subject from above.

Background: photographing your subject in a plain scene maybe in front of a white wall. or cropping out your subject and putting it on a black image.

Depht: including objects in all foregrounds, the front the middle and the back. it creates an obscure image with lots to look at.

Framing: allowing your subject to be in between two objects that create a frame around the picture like trees.

Cropping: cutting out excess space around your subject to create more focus and attention.

Experimentation: take pictures of anything and anything to see if you can create or find a new composition and take advantage of the fact that you can take tons of pictures, view and delete the unwanted ones in an instant.