Watch a lot of classic b&w movies -- you'll see that the issue, when the entire frame is monochrome, is avoiding muddiness (too much even greyness) and directing the eye to the subject, and separating them from the background.
To avoid mud, you need a black and a white reference somewhere in the frame. Besides lighting, it helps to dress actors with some pure black and pure white area in the wardrobe (I don't mean make large areas of set dressing or wardrobe black or white, I mean small accents like a black tie, white collar, etc.) You often see small hot spots from wall sconces or table lamps, streetlights, etc. to create a bright spot in the frame.
As for separation, backlighting is the most common technique, as long as the background is darker than the white edge you are creating. But you could also do it by framing dark against bright or bright against dark -- you don't always need to backlight. You have to think in terms of tones.
As for directing the eye, lighting can do that (important area in brighter spot of light, for example) and strong compositions. Think in terms of bolder graphics, like an ink drawing or b&w comic book would do.
Of course, there are always exceptions to the rules. 1930's b&w movies were softer and gauzier, with shallow depth of field for a romantic look; 1940's movies got higher contrast, with strong separations of bright and dark, but some French New Wave and British b&w movies of the 1950's and 1960's opted for softer lighting for a greyer but more natural look.
