I agree with the thoughts expressed already.
1. Point of view- make sure that your angles are flattering and/or interesting. With kid or pet pictures, standing over your subject and looking down is not likely to yield the image you are after.
2. Background. Watch for clutter. As the photographer, you are responsible for every square inch of your frame. Some thing can be 'cropped out' later, but some things should just be avoided altogther. In addition, look for interesting or attractive backgrounds. This might be in the form of shapes, colors, nature, use your imagination.
3. Understand the exposure triangle. Every image contains a choice of the three primary variables of an exposure:
- shutter speed
- aperture setting
- ISO
varying these parameters can have a profound effect on your ability to craft your precise image. Whether you want to freeze or blur motion, catch the background in focus or blur it out- there are ways to accomplish this. Learn them.
4. Think about light. This might seem obvious, but photography is all about light. Whether you are using natural light, interior lighting, an on-camera flash, or other lighting rigs, the quality and style of your image depends upon light. Shooting outdoors in the early morning or at sunset can yield entirely different tones and looks than indoors, or outside at noon. Also, the positioning of the light is key. For example: do you want a silhouette? Get the light behind your subject. Do you want to avoid silhouetting your subject but the light is necessarily behind your subject- use a fill flash. Learn about light.