Hey Jason - thanks for your email. Discovered is a tricky word. If you mean do people get discovered for films and TV when they are just sitting around somewhere, hanging out? Or walking down the street? Maybe one in a million.
Seriously. In the old days, even before my time, the studios had talent scouts that went to beauty contests and sporting events to find potential talent to be tested at the studio. And sometimes they even found talent at a soda fountain or by simply walking down the street.
But those days are long gone. You can figure that anybody who approaches you in a mall or somewhere and asks you if you want to be an actor / star, is probably going to try to scam you in some way - usually for money or sex.
But if you mean do people get offered representation, or parts in a film or show, if they are seen performing in something? Yeah, that happens. In fact it's pretty much the only way it does happen. You have to be doing something in order for someone to discover you. Let's take a look at what that means.
Below is a list of the types of things you can do to get "discovered." I've listed them in order of their strengths, but some of them are very close. Having a good role in a feature film (even a ultra low-budget one) that does well at festivals will probably get you some real attention. Doing extra work or short films are the least likely ways to get discovered. There are exceptions to this, but not many.
Note: I was an exception to this - I was interviewed for an extra role and the producer saw my interview and brought me in to read for a principal role, and cast me. But like I said, it's really rare for that to happen.
So, here's my list:Making your own ultra low-budget feature video and entering it in contests and festivals
Doing stand-up comedy
Doing your own thing on the internet (mainly YouTube or Funny or Die.)
Performing in a play
Doing improv and/or sketch shows
Singing in a club / cabaret
Doing extra work on films and TV
Doing student or short films
A last note about the list - the stuff has to be of good quality. If you're doing stand-up comedy and you suck (sorry to be blunt), you're not going to get discovered. If the film you're in is horrible (and not in a good way), it's not going to help your career.
And finally, even if your web series on YouTube is great, people have to see it, which means you also have to promote the hell out of it. Felicia Day went all over town putting up fliers for "The Guild" before it took off and helped her career.