If you have an experienced shotgunner handy to instruct you, that would be one way to get started. Failing that, I'd suggest you start with a Hunter Safety course, or your state's equivalent, if you haven't ever had one. Safety First...
I'd suggest you look next at
http://www.nrainstructors.org/CourseCatalog.aspx to see if there's an instructor near you teaching the basic shotgun class- there's a class locator at that site.
#1 thing is to absolutely 'groove' safety and safe gunhandling. That is critical. You have to be reliably and dependably safe in your gunhandling, muzzle control etc. or you are a danger to yourself, your family and innocent parties anywhere within range.
#2 thing is to learn to safely run your gun administratively. By that I mean to safely load, make ready to fire, fire, fire again, make safe, and unload the gun. Plain ordinary target shooting, shooting hand-thrown or machine thrown clays etc. will help with that. But you need to be fully familiar with the safe operation of your gun and capable of performing the steps above without problem in a non-stressful environment. That's 'learning to shoot' with a shotgun.
After you learn to shoot a shotgun, it's time to learn to FIGHT with one.
First take a gander at
http://www.thehighroad.org/showthread.php?t=396584. It would help to know where you are, but it isn't absolutely necessary. If I haven't covered your state in depth yet, let me know and I'll see what I can do.
The shortest way to climb the learning curve is at the hands of a good instructor. But you want to be
ready for a class of this nature. To be ready for such a class, you need to have safety down absolutely bone solid, and you need to be able to perform the basic tasks of shooting your shotgun safely and dependably. If you are unsafe in a class with a professional instructor, that instructor will toss you out unceremoniusly. If you are unable to manage your basic gun handling, you will slow down your own learning process as well as that of the rest of the class.
The basics are just that- basic. Nail down the basics first.
Can you win a gunfight without professional level training? Sure, it's possible. The odds are you'll never have a gunfight to start with. And beyond that, the odds are that you can prevail with even minimum preparation. But what I usually try to point out in situations like this is that it's not the odds which matter. It's the STAKES. Think about what's at stake here.
Do you have a home defense plan that places all your family members safely under cover, with you and your shotgun between them and any possible danger?
Do you know when you can legally and justifiably shoot an intruder in your jurisdiction? Can you control yourself well enough not to act out of raw fear?
Do you know how best to establish your household defense in order to give you the edge in the event of an intrusion?
Do you know how to conduct yourself in the aftermath of a defensive shooting?
You can learn those things to a degree on your own, from books, videos etc. But working on your own or with a friend cannot put the pressure on you that a good instructor will, as your skills are built one step at a time. Gunfights = pressure to perform. IMHO it's better to first experience that pressure on the flat range than with lives at stake.
It's better to learn things like the fact that a 12 gauge shotgun shell will go into a magazine tube just as easily backward as it will forward on the flat range, even if it does make you look like an idiot in front of a class as you take your gun apart in order to clear the jam it caused.
It's better to miss an easy shot on the flat range because you rushed it or didn't follow through when a little pressure was on than it is to make those mistakes in real life.
It's better to short-stroke a pumpgun in a multiple shot drill in a class than in a gunfight. And so on.
I'm a firm believer in training. I spent years as an EMT, on a volunteer basis. I was trained to state standards, like everyone else who wore that blue star. I spent a few years as a volunteer fireman. Likewise- training according to state standards, just the same as paid firemen. I spent a big part of my working life training soldiers- not just any soldiers, but Special Forces soldiers. They don't just put on a uniform and a funny green hat and take off for parts unknown- they get trained first.
Can you do what you need to do without ever parking your butt in front of an instructor in a formal class? Sure, it's possible. But ask yourself- is 'possible' really the way you want to go at this?
Stay safe,
lpl