The DRV8825 is a good choice for driving a bipolar stepper at 24V and 1A. I link to Pololu because the page has lots of information on the driver's use, but they can be found on Ebay for less money. The 5V power for the driver can be from the Arduino 5V.
Robin2's stepper basics might be of interest and the simple stepper program to test your stepper.
The AccelStepper library is widely used.