Producer, Assistant Director of Operations for the 48 Hour Film Project, and owner of Gorilla Film School, where real filmmakers will show you how to make films real fast
The very best way to learn about filmmaking is to jump right in and start making films. As many people have already mentioned, there is no better time for people that want to make films. There are tons of free resources out there--blogs, podcasts, and books are a great place to start. I always recommend starting with "Rebel Without A Crew" by Robert Rodriguez. It's not so much a how-to production book as a guide to the spirit of low-budget independent filmmaking. If nothing else, it will inspire you through the tougher times in the beginning when you're just learning how things work and are getting your feet wet.
Regardless of whether you want to shoot and/or produce this yourself, I'd recommend working on a film first, though I would actually recommend NOT working on your own film. You should really have the experience of seeing what it's like on set and how directors, cast, and crew all work together to bring a film to life. After this, you may find that you want to change things about your screenplay based on your experiences. If nothing else you will have a better understanding of the process of bringing your story to life.
There are many ways to get involved in a project without spending a lot of time. I always recommend the 48 Hour Film Project (www.48hourfilm.com) if there's a competition close to you--it's only a weekend, and you'll end up with a finished short film that will screen theatrically. Plus it's a lot of fun, and one of the best hands-on learning experiences (as a disclaimer-I work for them). If you don't want to go this route, do a quick search of film groups in your area, or get in touch with your local film commission--many groups have different networking events and meetings where you can meet other local filmmakers with projects you can get involved with. Or if you'd really like to get the best hands-on experience, make a short film yourself--you can do amazing things with an iPhone, and there are tons of free or inexpensive apps out there for editing and post-production. It's a great way to get your feet wet.
Regardless of how you start, the most important thing is that you actually DO start. Get involved in the film world and you'll find many great people and resources that can help you out. Best of luck to you!