Building and flying radio-controlled (RC) aircraft can be a fun hobby. It can also be expensive. The basic idea is to build a model aircraft from a kit and then find a place to fly it.
The easiest way to get started is to find a local field where people are already flying and find someone to train you. You may think you don't need to be trained but, in truth, you do. Even experienced pilots need to be trained in order to fly these planes. The reason is that you aren't inside the cockpit of the aircraft; you are standing on the ground watching your plane from the side, and it's easy to lose control.
So now that you've found someone to train you, what next? You need a plane. The best way to get your first plane is to either buy a used one or to have an experienced plane builder help you. If you decide to build it yourself you will need a kit for a trainer aircraft (US$50 - $60), a radio (US$50 - $500), an engine (US$80 - $100), a charger (US$20 - $30), a tool box (US$15 - $20), fuel (about US$12/gallon), and covering (US$10/roll). All these prices are approximately correct at the time of writing.
The kit should come with all the instructions you need to put it together and get it ready to fly. In the USA you need to register with the Academy of Model Aeronautics (AMA). To do this you need to find a model aircraft magazine and fill out the form there, or visit AMA's home page.
After you learn the basics of flying you can really have some fun. There are so many different models of planes out there so the possibilities are unlimited. Also, many fields hold contests that allow pilots to compete for prizes. It is also a great hobby for kids as they usually pick it up faster than adults and can end up teaching their parents, instead of the other way around. Just make sure you have fun.