This is easy.
Yes, velvet works, but on a budget it can be expensive, and I find that standard black cloth from Wal*Mart works fine.
How you do this:
Buy about 3 yards of black cloth. It will cost you around 9 dollars. Hang it in a way so it's about 3 feet higher than your tallest buddy (If it's a standing portrait, hang it just as high as your tallest friend if it's sitting), and make sure that any noticable folds are nearer to the bottom.
Then, position your buddy 3 to 5 feet in front of the backdrop, either sitting or standing. This is so when you light him/her, none of the light will spill onto the background, making it look brownish.
Then, take whatever kind of lighting you are using (Hopefully some kind of strobe or tripod based modeling light) and point it directly at the side of the face you want lit. If you're using a lamp or something, try and make some sort of blocker to keep light off the background but still on your buddy. Make sure there is a decent amount of light.
Then, on the other side of him, use some sort of black fill card (Foam board from wal*mart also works very well when you are on a budget) and have someone hold it as close to your friends face as he can without getting the card in the shot. That will keep light from bouncing back and lighting the other side of his face.
Then, shoot the portrait, but underexpose by one stop. That will allow the black to stay black, but the lit part of the face to retain it's features. If the end shot is too dark on the lit side, use the same camera settings but with more light.
Hope that helps.