How To Learn To GM
There are a variety of resources nowadays that can help you accomplish this. There are also many existing questions on this site about GMing that will point you to more content than you can ever consume.
Watch
In your question, you mention wanting to see more examples of real play. There's a number of ways to do so.
Actual Play Resources
- Podcasts capture the entire play session. There's video podcasts too like on Twitch. See Where can I find actual play podcasts for RPGs?
- Session Summaries (aka Actual Plays, Story Hours, Campaign Journals) usually are severely abridged, but leave out a lot of the cruft. See Where can I find transcripts of actual game sessions? and Where to find game session reports?
- Blogs. There's a million blogs about how to GM. Start with the RPG Bloggers Network. Go to the blogrolls of blogs you like to find more like them. Focus in on blogs about your chosen game(s) and play style(s).
- Play by post forums. If you want to watch people actually play in text, there's a million of these too. Many dedicated sites, specific forums on RPG.net, ENWorld, Paizo, etc. In fact, RP-by-post is very popular even when not affiliated with a proper RPG/ruleset.
- Sit in. There are plenty of other people running games, some in public places like your friendly local game store (D&D Encounters, Pathfinder Society) and conventions. See below under "Play" though, if you're going to the effort of being there you need to stop being a wallflower and get on in and play.
Some games also have better advice sections than others - see What role-playing games have good gamemaster advice sections?
Play
In the end though just watching is not the most effective approach to learning. Watching games is less useful experience than actually being in one. Have you considered playing in those games before running them to learn from other GMs? It's reasonably easy to find other gaming groups, you don't have to abandon yours to play in another. Where can I find other RPG players?
Go to RPG conventions, find games at gaming stores, play on forums or G+ (see also Finding online RPG players for a play-by-chat RPG Campaign?) - just get more experience. The GM was often called the "judge" in the old days, and in the legal world you need to spend a lot of time being a lawyer before you make a good judge. You need to spend some time playing to become a good GM. If you can't think how the players will proceed in a given situation, you need more play time.
Read
There are many books on GMing - see What is the single most influential book every GM should read?
Also try watching/reading relevant genre media. "I don't get how to put together a story" should get its first-order correction by consuming some of that genre and looking at the stories.
Learn
A lot of the problem you seem to be experiencing is pure storytelling. Try How do I get better at narrating/storytelling as a GM? and As a GM, how can I create and role-play diverse NPCs better? Read up on the specific aspects of GMing you feel you're not good at, there's plenty here. Try questions tagged with the gm-techniques tag. Feel free and ask questions here as well about specific aspects of GMing.
There are also a large, large number of RPG forums out there in the world, for every game and type of gaming. If you don't understand something someone posts, you can easily reply and ask.
Do
aka How I Learned To GM
We didn't have these newfangled Interwebs when I was a kid. I GMed almost before I ever played. I did play in a very informal game of D&D in a car on the way to Scout camp, no dice, PvP, everyone had artifact weapons. But other than that, I started out as a GM. I bought a sci-fi RPG (Star Frontiers) without knowing anything about it (I had bought and played a little TSR chit game, Star Force, and was looking for other fun stuff from the same company). None of my friends were interested in GMing and I was in a small Texas town that didn't have conventions or whatnot - life was less mobile and connected back then. So I just read the game books and then ran games for my friends. And I kept running them, and learned from my mistakes and corrected. I read comics and science fiction avidly, so characters and plots weren't that hard to devise. Beyond that, I just learned the way you learn to do anything through practice, whether it's a sport, writing, a musical instrument... How-to's and YouTube videos are cute jumpstarters nowadays, but "Do, and learn from doing" has yet to be eclipsed in being the primary way to actually become good at something.
Fear of "making a mistake" is the dumbest and most paralyzing instinct you can have in life. In a video game you're going to die a couple times off the bat; in baseball you're going to swing and miss a lot before you hit; in baking you're gonna burn some cookies. But you learn through those mistakes. It's fine to do a little reading up ahead of time but the only way to become good, really, is get your butt in gear and do it.
Dungeons & Dragons Basic Rulebook (1981, Gygax & Arneson), pg B60:
Your character doesn't know that
A player should not allow his or her character to act on information that character has no way of knowing (for example, attacking an NPC because the NPC killed a previous character run by the player, even though the NPC and current character have never met). If the players get careless about this the DM should remind them. The DM may, in addition, forbid certain actions to the characters involved. The DM should make it clear to the players before the adventure begins that characters may not act on information they don't have. It will save lots of time later.
In my experience (and I started playing in the 80's with the Basic Set referenced), it has always been bad form to use out-of-character information. Reading an adventure module or studying the Monster Manual just to get an edge was frowned upon.
"Metagaming" apparently originated in military/political theory (Wikipedia),
via the work of Nigel Howard (Wikipedia), published in 1971. This original use of "metagame" doesn't seem to match the way we're using it in roleplaying, and I can't find a source for where it began to be applied to "using out-of-game knowledge in-game".
Wikipedia also has an article on metagaming in roleplaying. It may not add anything useful to this discussion, but I include it for completeness.
It's worth noting that not all game systems (or communities) consider metagaming to be a bad thing. Generally, this is when meta information is used to improve play (as in many storygames, where players may intentionally have characters make sub-optimal decisions to complicate the story in an interesting way), as opposed to the player gaining an advantage.
Best Answer
Perhaps this exists in earlier games, but Dungeon Crawl Classics, first published in 2012, makes this explicit.