Domesticated animals such as cows, horses, rabbits, poultry or sometimes even cats will not always remain calm and stay in the right position while you take photos. As a photographer, you have limited influence over how an animal poses or moves. So you need to set yourself and your camera up for action. If you shoot at 1/1000 of a second, you can capture even tiny movements in focus. If the lighting is a little low, I increase the ISO setting until I can get the aperture and exposure time that I want. The aperture controls the bokeh (blurriness) in the background. Choose the aperture setting to determine whether your whole cat is in focus or just its eyes and whiskers. If the aperture is wide (e.g. f2.8), the depth of field for a cat portrait is just a few centimetres. With the aperture closed (e.g. f18) the whole cat is in focus. As well as the light conditions, the camera settings of exposure time, aperture and ISO also have a considerable influence on the results. So I recommend not working in automatic mode, but preselecting the aperture or timing or even working completely in manual mode. If the subject moves while I am taking pictures, I set the exposure time, while if it is calm, I preselect the aperture. I find a tripod gets in the way a bit for fast work, so I prefer to work without one.
Set the autofocus on your camera to the smallest setting so that you can focus sharply on the eyes, for example.
The background is the stage for your subject. Make sure it is not too busy or cluttered. Lots of details in the background can distract from the subject and can be annoying. With staged photos you can choose the background, but this is not possible for spontaneous, natural shoots.