Instructables member 'homunkoloss' describes in detail what needs to be done to control a single relay with an Arduino board. Using relays makes it possible to control much higher voltages and currents than is normally possible with transistors or an Arduino itself. He includes the theory behind the component selection and includes a schematic and example sketch.
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Although the process described above may be simple for one relay, or if you have plenty of time - it can be done reasonably easily. However if you have two or more relays - it's much easier to use dedicated relay control boards. Here at Freetronics we have the RELAY4: board, perfect for controlling up to four relays with Arduino (or any other microcontroller's) digital output pins:
Or if you'd like to control up to eight relays - or more at once with an Arduino Uno orcompatible board - consider our RELAY8: board. Controlled via I2C, you can stack up to eight shields with the appropriate power supply to support 64 relays at once: