Qualifications
You'll want to score at least a high school diploma if you hope to make it in the field. That knowledge of math and computer applications will come in handy when you step into your first position (source). You can also get a leg up by attending a woodworking program at your local technical school.
While there are no specific certifications required of woodworkers, there are certain certificates you can earn to give yourself a competitive advantage. They include a national certificate through the American Woodworking Institute and five stages of certification from the Woodwork Career Alliance of North America (source).