Submission wrestling is one of the oldest sports in the world. It is very different than professional wrestling and if you want to be good at it, you have to prepare yourself both mentally and physically.
The best way to do that is to learn one of the martial arts which form the basis of submission wrestling. A few examples of these include Brazilian Jiu Jitsu, Catch Freestyle Wrestling, Judo and Sambo. There are many schools these days so you wont have a hard time finding one.
As a beginner, your first few sessions will involve watching how others do it. There are also videos around which you can buy or just watch using your computer. In fact, some of the best fighters watch previous matches that they participated in or watch their fellow competitors so they can find a weak point that can be exploited during their next match.
Since you learn more by doing it rather than watching, put theory into practice by sparring with another wrestler.
Keep in mind that people get hurt in submission wrestling even if it just a sparring session. One way to prevent that is to get yourself used to the idea of falling down or being held in a certain position....