The Rule of Thirds:
The rule of thirds is when important subjects in a photo intersect with the corners of a grid made up of nine squares. If that sounds confusing, the bottom line on the grid lines up with the horizon on these photos.
Leading lines are lines in a photo that draw your eye in though the scene in the photo, or alternatively, towards the subject.
Symmetry and Patterns:
Symmetry and Patterns are pretty self explanatory. To create tension and make a photo more interesting, photographers will break symmetry by introducing something that is unsymmetrical.
Your viewpoint is were you take the photograph from, the viewpoint can have have an impact on what kind of message the composition has.
The background is what is behind the subject in your photo, a busy background detracts from the subject were as a a plain background adds emphasis to he subject.
Depth is hard to convey in a photo, as it's a 2D medium. So photographers use overlapping a focus to convey depth.
Framing is using natural objects to create a border around the subject of interest, sort of like a picture frame.
If you take a photo that has a lot of extra space that takes away from the subject, cropping is a great way to return focus to the main subject.
Direction Of Motion:
In a photo, it can be hard to convey motion, so a photography will use techniques like panning to show motion.
And finally, experiment! Break the rules! Or, YOLO, as the kids say.