Camera Composition

Rule Of Thirds:

If you move the subject from the centre to where the lines of the grid meet, the shot appears more balanced because where the lines meets are our main points of interest.

Camera Height:

Rather than tilting the camera downwards to look at what's on a table (for example), it is more interesting and unusual to bring the camera downwards to the same height of the subject. It adds more visual interest and provides more detail when looking at the photo.

Depth:

Having something in the foreground and background creates a deeper depth of field rather than focusing on something in the foreground, making the depth appear shorter from the perspective of the camera.

Backgrounds:

Used in combination with he depth of field, it can make basic shots appear more interesting. Textured or backgrounds that aren't necessarily flat can add more visual interest depending on the desired aesthetic. 

Lighting:

Even without professional lighting, using things such as a television screen paused on a particular moment can provide a natural (or unanatural depending on the color you have chosen) hue. Using windows and natural light can also be more interesting than house lights.

This is my favorite photo I took in terms of the rule of thirds, camera height and depth. Lowering the camera height to the height of my dog allowed a more visually appealing photo and emphasizes the detail of her fur and the snow. There is a decent depth of field as you can see the trees on the right hand side in the far background against the closer bushes on the left hand side. I also placed her head in the top left corner of the grid where the lines meet as suggested in the tutorial.

In my opinion this photo has quite a short depth of field as the body of Casper is cut off, creating a 2-dimensional visual effect rather than a deep photo. He is also placed in the centre of the grid, although it makes him the centre focus, it isn't that interesting of a photo. I think that the photo of Jess (below photo), the black and white dog, is an improved version of the same shot in terms of the depth of field.

(similar to shot above but from a different angle)

Although this photo has a very short depth of field I like the emphasis that is placed on the colors of his fur and the prominence of the heterochromia in his eye.