Use a wide aperture when you want to isolate your subject and throw a distracting background out of focus. Apertures like f5.6 or wider will usually do the job, especially if your subject is located a good distance away from the actual background. If your subject is a person or animal, focus on the eyes. It is often better to frame the subject against a dark colored background in order to capture the greatest degree of detail in your subject. Use a tripod whenever you can.
Nothing beats a strong, heavy tripod in delivering sharp telephoto shots.