Odds of Getting In
Breaking into upholstery is as simple as grabbing some nail pliers and deconstructing your parents' dining room chairs. It won't pay anything and most likely will get you grounded, but it will provide valuable experience. Other than a high school diploma, the only obstacle for the average person to get hired as an upholsterer is a little bit of experience.
Some people are fortunate to have a relative or friend who owns a shop and is willing to take on an assistant. Others get a book or study DIY websites online and work on their own furniture or, if they don't want to tear up their own couch, something the neighbor discarded. Another viable route is to take a course at a local vocational school or community college. Any way you can get some experience will help you land that first job.
Many employers, especially furniture makers, only require one year's experience, and a few will train newbies. These jobs tend to turn over quickly, as they are pretty repetitive and basic.
Once employees get enough experience, they often move on to more challenging and diverse jobs. That leaves the door open for you to come in, start building your shop chops, and get a headstart on that experience you need to jumpstart the rest of your career.