Qualifications
This is a serious business; so serious, in fact, that it's regulated by the Federal Aviation Administration. The FAA requires that all aircraft maintenance be performed by a certified aircraft mechanic or by someone under the mechanic's supervision. You'll find two types of certifications: the airframe certification and the engine, or power plant, certification. Most airlines and maintenance shops want mechanics with both certifications (source).
What are the actual qualifications? You must be at least eighteen years old and able to speak (and write) fluent English. You also need at least thirty months of documented experience working on airframes and engines. No, that requirement doesn't mean your friend with an airplane watches you change his oil. You must work under the supervision of a certified aircraft mechanic, and your time must be verified by someone authorized to do so.
Thirty months of work experience will take you roughly two and half years. Feel free to double-check our math. Don't even think of getting someone to fudge your experience records; the FAA doesn't look very kindly on that.
However, you do have another option. The FAA will accept your completion of an FAA-approved aviation maintenance school program instead of the work experience. These schools typically last eighteen to twenty-four months, and may be stand-alone technical schools or affiliated with a local community college. Instructors will combine classroom instruction with hands-on practice on actual aircraft. Some instructional segments will challenge you more than others.
Fast-forward to the end of the process. You've completed either the work experience or the aviation maintenance school requirements. You still have to pass the Airframe and/or Power Plant Exams. Recognizing that not all test candidates are equally prepared, test-prep schools have sprung up throughout the country. These short, intensive courses drill you on the actual types of questions you will encounter on the FAA's certification exams.
While test-prep courses may provide useful reinforcement, these schools have often been criticized for churning out test candidates who will pass the exams but are ill-prepared to perform the actual work. If you choose this route, evaluate the school carefully; don't fall for a promise of a "guaranteed" result. You'll also have a practical exam with a certified examiner, and you're going to want to be prepared to pass that one, too. The examiner guy won't be as generous with the shortcuts.