You must carefully remove the motor from the hard drive case to use it. Most hard drives use small torx screws to hold the case together, and removal requires inexpensive torx drivers, which you can purchase from hardware or electrical supply stores. After taking the case apart, you'll carefully cut or desolder the connecting wires, leaving as much of the wire connected to the motor as you can. Some hard drives have plug-in connectors on the motor leads, which makes the job even simpler, as you just unplug the connector.
For project use, you will have to design or obtain a stepper motor controller. Each coil connects to an output terminal of the controller, and the programming drives the motor. The website of California State University, Long Beach, hosts a tutorial on how to do this (See Resources), but controlling the stepper motor requires an in-depth knowledge of electronics. The best feature of stepper motors -- accurate position control -- lets you instruct the motor to turn, for example, 100 times and stop. For this reason, stepper motors play an extensive role in robotics.
If you spin the shaft, the motor becomes a generator, and produces a voltage output. Because the motor is small, the voltage output is not significant. However, you can can drive small LED lights, make a windmill out of it or attach the motor to a small model steam engine. The key is to experiment, and find out how you can spin the shaft, with an overall goal to determine the maximum voltage output with a shaft-turning input. The Technical Library offers some simple output circuits to obtain a smooth DC output voltage, and an electronics technician can assist you with the wiring.
To determine the motor's coil specifications, you need to contact the manufacturer of the hard drive from which you removed the motor. The manufacturer may consider this proprietary information, however, and refuse to share it. If so, a qualified electronics technician can assist you in determining which coils line up with which output pins.