With so many types of lights and the infinite number of setup combinations, studio lighting could be the subject of a book. In fact, there are several books dedicated to just that. However, if you're interested in investing in some studio lighting equipment, there are a few basic things that every photographer should know.
With a good set of basic lighting tools, you should be able to shoot in most types of situations and subjects. Here is a run down on the most common types of studio lighting.
These are the sorts of lights you may associate with movie production. Continuous light simply refers to light that is always on (as opposed to a flash which is there and gone).
Though this method can generate quite a bit of heat and definitely uses more power, it is a great way to work subtle lighting situations. Since you can see the way your lights interact before you shoot, you will have a good idea of what the photograph will look like beforehand.
You can pick up a simple kit for continuous lighting online for a pretty reasonable price. Most photo stores on the web have a section dedicated to studio lighting equipment, so from there its mostly an issue of what you're willing to spend.
Look for a flash kit that has light stands, light fixtures, bulbs and a reflective umbrella. Continuous light can be provided by fluorescent, halogen, and tungsten light bulbs which you use is going to be a matter of taste and tone.
As you may have guessed, this type of studio lighting equipment is dedicated to setups that utilize a flash like those used in fashion shoots. With flash setups requiring low amounts of power and generating even less heat, they are usually the best option when shooting human subjects for extended periods of time.
You can get flashes in either moonlights or flash systems. Moonlights require only syncing to the camera while power-pack flash systems will have a central power point to which the flash heads connect.
Similar to continuous lighting, there are plenty of ready-made flash kits available for the choosing. Be sure they have lighting stands, umbrellas, modeling lamps (these allow you to preview your lighting) and the sync cords required to ensure your flashes fire at the right time.
Flashes with sensors that will fire with your camera flash are the easiest to use, but may run a little deeper into your pocket.
Its worth noting that combining these two studio lighting methods is one of your strongest options. This will help you have lots of flexibility in your shooting so you will be up to the task no matter what comes your way.
With basic kits starting as low as $50, you should be able to get some pretty decent studio lighting equipment setup with a low initial investment. However, if you're on a super small budget, you can always look for used kits and get creative with lights you have around your house.
Now that you have a good understanding of the most common types, have fun shooting and getting great portraits.