There are several ways to make a Stepper Motor run, and the best way will depend on the application, the motor and the electronics available. For running a stepper motor from an Arduino these are the main ways to go
1. A ULN2003 Darlington driver board. Typically sold with small geared steppers this requires four digital pins and the Arduino sketch needs to directly drive each coil
2. A driver board/shield with a constant voltage driver, such as the Adafruit Motor Shield. This runs over SPI (so only needs two pins) and can run many kinds of steppers and normal motors fine, unfortunately it couldn't run my steppers.
3. A 'chopper' driver that will vary the voltage to keep a constant current, such as the A4988 or the DRV8825 chip, either direct or via a board/shield such as the Stepstick or Pololu.
I wrote an instructable that covers the third method, running one or more steppers via an A4988 IC on a StepStick board. See it here