Rule of thirds, golden ratio, golden spiral, triangles, diagonals. Use them, love them, and then break them as necessary.
These are snapshots, really. RoT would have worked, though so would good use of the golden ratio, had the dog been shot from the right of where the camera was positioned (using the tree to add some interest to the background, and partially frame the dog's head).
Simply, get used to using these rules/guidelines for composition. Once you have them down solidly, you will know when to bend or break them to make a better image. (e.g. abstract photos rarely obey any of those compositional rules, and if they do, they probably don't need to)