Horse clipping/braiding business?
Ask a farrier to take you under their wing. For the first few months the only thing they will let you do is hold the tail while they take pictures but that is 90% of the job anyways.
Judy and the Beast
You asked how to get experience. First, I would ask to practice on horses who have been braided recently. They will have manes pulled to the correct length and (hopefully) be familiar with how to stand for braiding. Then, I would volunteer to braid a few manes at a few schooling shows. Take clients who go to the "real" shows and might use your service for real. Realize that it will take you about 10-20 times to get marginally decent at braiding. Clipping practice will be harder to find as a bad clip job is hard to fix. Ask if you can practice on some schooling horses who they are often not as fussy about how they look. Or, put up a flyer advertising your service at a local barn. Be honest about your level of inexperience and charge a very very cheap rate until you gain experience. Remember some horses need to be tranquilized for clipping the sensitive bits.
The best way to learn to braid is to start going to shows and putting the word out that you're available. As you gain experience at it, you'll get more clients, because a lot of trainers will gladly pay for the services of a braider. It saves them time and hassles when they don't have to worry about this themselves. Make sure you go to the recognized shows rather than the schooling shows, because these are the shows which mandate braiding.
Most people clip and braid their own horses tail so why hire someone to do it? Maybe it's a thing in the US I don't know. I'm not a fan of braiding but it depends on what for. I've seen people who braid their horses forelock and tail to put them out in the pasture. They seem totally ignorant of why those things exist on a horse.