Diagonal lines can be used as leading lines. They move from one point, usually to a central point in the image. This leads your eyes all around the photo, bringing your point of interest from the center to different points. Here are some examples of Diagonal Lines.

Horizons can create a contract, or a smooth photo that is pleasing on the eyes. Horizons are usually of Landscapes, though you could be using a desk, counter, or some surface to act as a horizon line as well. Plenty of colours, pleasing smooth lines, and possible contrast makes Horizons very nice to look at. Here are some examples of Horizons.

The rule of Thirds is a trick you can use with your camera. If you're on a setting that gives you a grid, like this..

This is your grid of thirds. It can help line things up, but the real trick is that you want to get your central points on one of the intersections. Set your focus to pinpoint an object in your intersection to blur out the rest, and enjoy your pulling photo.

With these photos, we've got one depth of field / Rule of thirds, with the baseball photo. Attention is immediately drawn to the object in focus, and in the corner. With the next, we have a dandelion sitting or growing through some planks. We have a flat background for this photo, but with the use of contrasting colours and the Rule of Thirds, attention is once again drawn to the flower. Positioning your object right in an intersection can make the photo look more neat, having a background with something in the corner.