IGN has an article about custom markings on your Pet in Create A Pet.

Looks like IGN was too lazy to make their own video.

Once you’re done editing a layer, in order to make a new marking of any kind, you must make a new, blank layer. Even if the two markings wouldn’t touch—such as a marking on the front-left paw and another on the front-right—each marking must have its own layer. To add a layer, click the + button below the layers list. The newly added layer will be listed as the topmost layer, but can be moved anytime.

With a new layer selected, you can select a marking from the list in the top-left corner. There are two modes here, selectable by tabs. The first tab allows you to select a premade mark in a specific body part, which is useful if you’re going for something realistic or symmetrical. You can either click your pet’s body part directly, or click the appropriate body part in the top-left “animal map.” If you’re playing with a large resolution, it’s probably easier to click the pet’s body because some parts of the animal map can be a little small.