Qualifications
A professional tailor's only as good as the framed degree they have mounted on the wall.
Said no one ever.
At the very least, a tailor should have a high school diploma or a GED. You'll need to have a basic understanding of mathematics at least. If you can't figure out how much total cloth is needed for pants with a thirty-two-inch inseam and a forty-inch waist, you're going to make a lot of customers very angry.
An art elective or a business class in high school will also help with the intricacies of having a tailoring shop. Sewing and design would be an even better idea—if you really want to go wild.
For the final product, it's experience that'll get you the job rather than any formal schooling (source). There are a handful of "official" apprenticeships for tailors that require between four and eight thousand hours of on-the-job learning. Though legit, these apprenticeships are incredibly difficult to secure. Make sure you show up wearing your best ascot.
Really though, just knowing what an ascot is should put you ahead of the curve.