You can achieve vivid black and white portraits with black backround without a studio or fancy monolights. I used an affordable softbox along with a mixture of Yongnuo and Canon flash technology.
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GEAR: You can capture an image like this with nearly any digital camera that allows you to control off-camera flash. My go to DSLR is my full frame Canon 6D. It's a work horse and handles whatever I throw at it. It's also excellent in low light so I can increase the ISO when I need to without too much noise. I used my Canon 50mm 1.4 lens to allow a little distance between my subject and I. I could have comfortably used an 85mm 1.8 as well. Both these lenses are prime lenses meaning they have a fixed focal length - They can't zoom but they're known for being quite sharp and they're affordable! If you're not familiar with fixed lenses, check out this post. To provide off-camera light, I used my Canon 600EX-RT controlled by a Yongnuo YN-E3-RT radio controller. The YN-E3-RT is an affordable alternative to Canon's ST-E3-RT and controls the Canon speedlites with ease. It also boasts focus assist lighting that the Canon version does not have, which helps focus during dark shoots like this. This setup allows me to control my speedlite wirelessly using the radio capability built into the speedlite. Earlier speedlites did not have this and required separate, battery powered radio receivers connected to the strobe. You could create the same light using Canon's more affordable 430EX III-RT. For my light modifier I used a convenient Neewer 24" softbox on a Manfrotto light stand.
SETTINGS: Since I am using a 50mm lens, I want to keep my shutter speed above 1/50 of a second, as a rule of thumb. 1/200 to 1/250 would have been ideal, but 1/80 worked. A common saying is that shutter controls ambient light while aperture controls flash. In reality, it's a little more complex than that, but the saying helps think through lighting setups like this. I used an aperture of 5.6 which will give me a little extra focus range in case either subject moves. If you're not trying to be creative with blur, an aperture between 7-9 is ideal depending on your lens. For ISO I went with 2000. The Canon 6D really spoils me with its ability to use high ISO without much noise. Ideally, ISO should be as low as possible for sharp, clean images. After the camera settings are selected, it's time to adjust flash settings. I adjusted the flash power while taking sample images until I achieved the look I wanted. Sometimes I do this in ETTL mode by adjusting the Flash Exposure Compensation (FEC) and sometimes I use manual flash mode. Do whatever is easiest for you!
TIPS: I shot these in my living room at night. The darker the room and background, the better. You could take photos like this during the day but you would need to increase shutter speed and stop down aperture to darken the ambient light. If there are any details showing after you capture the image, you can use the burn tool in Lightroom or other photo editors to darken them away and isolate your subject. For more details on isolating the subject using dodge or burn, check out this post. I placed the softbox to the right and slightly above the subjects in a position where it would not spill light only my background. These shots looked much more dramatic in black and white so that's what I went with for final edits.
SETTINGS: 1/80 sec at f/5.6, ISO 2000
SETTINGS: 1/80 sec at f/5.6, ISO 2000
Feel free to ask questions in comments below!