For a hobbyist or someone just starting out, the cost of renting your own studio space can simply be too much or something not yet justified by the amount of time you spend on photography. This great video shows how one photographer made a studio space out of a small room in his New York apartment.
Coming to you from Jeff Rojas, this great video shows how he turned a 6-by-10-foot room in his apartment into a studio. It can be easy to think that you need a lot of space for a studio, and while that's true in certain cases that depend on what and how you shoot, you can accomplish a lot than you might think in a space that's just the size of a typical college dorm room. If you have a spare room in your house or apartment, I recommend following Rojas' model. Having a workspace available to you 24/7 is very freeing creatively and allows you to shoot and experiment at your leisure without time or financial pressures. However, if you decide to also do client work from your home, I recommend speaking to your insurance company first and carefully considering the ramifications of bringing strangers into your house or apartment. Have fun and be safe!