When you're first starting out with artificial lighting, the sheer range of modifier types and sizes can be a bit daunting. This helpful video will show you some of the basic modifiers and how they shape light on a subject and the catchlights they create.
Coming to you from Pixel Viilage, this video will show you how some of the most common light modifiers affect the look of your subject in portraiture. In it, you'll see a bare reflector, beauty dish (with and without a diffuser), softbox, and two differently sized parabolic umbrellas. While the main thing you should pay attention to is how each modifier shapes the face (notice how the highlights and shadows bring out facial structure and look for where hot spots are created), the hardness of the light, and the fall-off, also notice the catchlight each modifier creates. The beauty of artificial lighting is the ability to have vastly more control over the quality and shape of the light. Of course, as you become more advanced, this is augmented by adding more sources, each with their own distinct modifier and power to precisely shape the light exactly as you please. I think you'll likely find it quickly becomes addictive learning about and creating different setups!