Despite the popularity of vibrant colors from even home printers, black and white images still are popular among many people. The B&W aspect of an image brings out a feel of traditional artwork dating back toward the beginning of photography. Black and White images often evoke emotion from a viewer that is not always possible when processed in color.
Since these days, I photograph people more often than other subjects, I will focus primarily on getting some good results when shooting people. Some principles to other forms of photography can certain apply.
In most cases, we are looking for a high contrast image. This means that a dedicated, directional source of light is ideal. Shooting people with natural light coming from a large window on an overcast day will probably not bring forth your best results. Also shooting with an umbrella will 'probably' have light so scattered that it will be difficult to control the direction of the light.
In many cases, a strobe with a reflector focusing the beam of light can be used quite effectively as in the diagram. A strip light with a grid can also be used effectively. In the top image, a strobe was placed camera right. Most black and white images are defined by areas of brightness and darkness (contrast). Since little to no light is hitting the model in the top image, there is a relatively clear border between the lightest portion of the image and the darkest portions. Since the wall behind the model was relatively dark itself, her back falls into nearly full shadow where her face and upper body appear relatively very bright.
The transition between darkness to light will also depend upon the size of the strobe and distance from the subject. Smaller light sources will create a much harsher contrast. Also, moving the light 4-5 feet away from the model will also increase contrast, whereas bringing it in close will result in a very quick fall off of light as it hits whatever may be behind her. Experimentation is often the best route here to decide how close to place the light source to the model.
Also important, when shooting people, position of the shadows and camera angle is important. Positioning the camera approximately in line with her shoulder allowed for capture of the 'contrast' line and curves highlight the pose. In most cases, camera crop will be fairly close to the model depending upon the purpose of the image.
In post production, your friends in Lightroom will be your shadows and highlight sliders. In Photoshop, levels and curves can be very useful in pinpointing exactly what areas that you want in shadow and how deep you want the blacks. Some photographers prefer texture to the skin, and will actually add grain (noise) to the image. Other photographers will reduce the clarity slider in lightroom (or use a small amount of blur) to create a much different look to the final image. In the end, the choice is up to your creative spirit!