Now here's some advice from someone who actually was an arm wrestler. Your question was very good about if you need a trainer or not. The best advice I can give to a person starting out is to search out arm wrestlers in your area or at least in your state (assuming your U.S). Training with other arm wrestlers is what the pros do as well as serious amateurs.
Training on that table is way above just what you can do at a gym, or just listening to people giving advice on line. You'll find arm wrestlers are down to earth people who'll be happy to work with you and teach you all they can. You'll also start to strengthen in areas that you've really never stressed before. That's important when that first 'hit' from a really good opponent shocks all the joints and tendons in your poor arm right at the start. More abuse follows (if you don't get flashed pinned) with severe straining, twisting and pulling in ways our bodies weren't actually designed for. And that was just your first skilled opponent of the day! You're going to realize fast that your not fooling around at a school lunch table anymore! Then it's on to the next crazy fast and strong dude.
Google Northeast Board and armwrestling (They wouldn't allow me to post the URL). It's the best website that I know of. You'll find practically all the arm wrestlers in the country are members there. Be prepared to travel up to a few hours to get to where your guys train. Let me know if you can't find people to train with, maybe I can help. Good Luck