Many of my basic business and personal portraits are done with one flash - often an "on camera" Hot Shoe style flash - but put on a light stand and bounced in an umbrella.
Using a flash cord, either a basic one that goes from the PC connector to the flash - or a dedicated one like Nikon has (other makes have them too) puts the flash off the side. By bouncing into an umbrella you get a softer light. Put the flash two or three feet to the side of the camera and up high enough to be about 45 degrees up from your subject and you can get a very nice shot.
This works well for one person. For more people I'll pull out my bigger flash system.
You can also put a silvered reflector exactly opposite from the flash (behind on the opposite side and slightly below) to put a nice rim light on the back of the subject. As Woody Allen joked in one of his early stand up routines - it give the illusion of three dimensions.
