If you want to become a video producer, your best bet is to get started with independent productions.
Look up the appropriate websites for your area where people are looking for film crew.
Even if you aren't going to get paid for it, you'll still be able to start putting your name to things, and start getting meeting the people in the industry. Be nice to everyone, you never know who's going to be in a position to give you a big break one day.
But mostly, learn and be useful to people and eventually you'll work your way up to where you want to be.