In biological imaging, telephoto lenses have several main purposes. The most obvious is to allow photographs of distant organisms to be made. Ideally, we would like to make all photographs with shorter lenses from close distances. Sometimes, however, the organism doesn't want you nearby, and will leave. Other times, you don't want to be too close to the organism! Telephotos have other uses, however. Equipped with extension tubes, they can also be used as long-distance macro lenses to photograph small but skittish organisms.
For more information about features and types of telephotos, go to the lens page.
A telephoto can be hand-held if the reciprocal of the exposure is greater than the focal length of the lens. For instance, if you are using a 400mm lens your shutter speed should be greater that 1/400 of a second, 1/100 of a second for a 100mm lens. Anything slower risks camera shake. Even at the recommended shutter speed you must be particularly careful to hold the camera still:
Newer lenses are incorporating special technology that minimizes the effects of camera shake and may allow you to handhold at speeds 1 to 2 stops below normal.
Sometimes it is difficult to even find the subject with the lens. One way to get better at this is to carry a telephoto lens (and camera) with you on bird walks. Even if you can't take the pictures handheld, you will get practice getting the lens on target. Keep your eyes on the subject as you bring the camera to your eyes - don't look down to the camera and then bring it up.
The focal length of a telephoto can be doubled by using a multiplier (extender). This will cost you 2 stops of exposure, however. For instance, a 400mm lens with a maximum aperture of f4 becomes a 800mm f8 lens. This lens will give double the magnification, but will need to use a shutter speed of 1/800 of a second - and will be less likely to be able to use that shutter speed because of the smaller aperture! Of course, you are going to mount this combo on a tripod.
If you want to use a telephoto on a subject that is too close to focus on, you can add one or more extension tubes. These simple tubes simply add length to the lens. This allows it to focus closer, but you can't focus on distant objects with the extender in place. Extension tubes do reduce the light hitting the film (but less than a multiplier does). Extension tubes can also be stacked. All of the problems with increased camera shake that apply to multipliers also apply to extension tubes.
Finally, remember that the telephoto is a tool, not a crutch. If there is an animal that you think you can get closer to, and getting closer won't endanger yourself (or harass the animal), then take an insurance shot from a distance and use your field skills to get closer.