You'll want to start by reading up on hobby servos, stepper motors, and DC gearmotors and how they're controlled. A little on robotics, too, perhaps.
Adafruit has a popular entry-level Motor Shield that comes with software and tutorials, check adafruit.com. Sparkfun has more motor control modules than you can shake a stick at, also with software: sparkfun.com. Pololu is a popular place for people building robots, which of course are all about motors; see http://www.pololu.com
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