There are professional wrestling training schools. They are much like any other training school and will give you the skills & dispositions needed to give it a shot. Look for a good training school that is affordable, puts on weekly shows (will get you seen), has connections and most of all has put out quality wrestlers into the world.
Like in any other job you start from the bottom in small companies, often amateur companies. Try looking for an agent, he might get you some contracts for fights. If you are good and fight somewhere where people see you you'll get offered better things.
First you'd have to get into a professional wrestling school (I recommend the one in Atlanta, GA). They will teach you mechanics, mic skills, and moves along with all the rest you need to become a wrestler. The "classes" are at night and they have something like what you would call a dorm. This leaves time for a day job.
There are two ways: being discovered, and if not, there are many training schools which you can go to. These are developmental camps where you learn the business, and from there, hopefully get discovered.
You should look for a good wrestling school in your area that has placed its graduates in local independent promotions. These schools should have a track record of having graduates make it to WWE or Impact. Be prepared to travel if needed.
I would start young. Start restleing for your middle school, than high school. If you were good enough then, go to college to wrestle. If you are great, you will be noticed by a drafter, and be drafted.