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.
The first thing to do is Find the Fun.
I ran a campaign in a bygone century with all brand-new gamers. They made every mistake in the book. But to this day, you get that gang together, and they will start laughing about every failed rescue mission and chaotic retreat.
They enjoyed the feeling of doing something entirely new and being a little at sea. Me leading them by the nose towards the right answers would not have been enjoyable for this crew.
On the other hand, if folks are getting frustrated and confused, then judicial hints are in order. You have the right idea, but don't let an NPC become too much of a hint machine — either the players will resent the “nanny” or they may become too passive and let the NPC guide them.
Can you adjust your campaign to their skill level?
How much help you need to give will partially depend on your campaign. If you are running a homebrew, you can dial back the danger so the party can survive.
If you are playing a published campaign (especially a non-introductory one) then the danger may ramp up more quickly than the players are ready to cope with. You might either need to give more frequent hints, scale back the hazards in they encounter, or hand out more treasure (like healing potions).
Are they missing out on whole parts of the game?
If the players are just not figuring out the basic things they need to do, and are missing out on part of the game, then a little guidance is needed. (Sometimes this happens when folks have played video game RPG’s, which provide a simplified play experience compared to “real” D&D.)
For example, players should know:
- There is secret stuff in dungeons they should search for.
- NPC’s are worth talking to. Unlike some video games, they may have more than one thing to say.
- Players can contribute to the story, rather than just waiting for it to be revealed.
- Combat is tactical; a plan can be important.
There are tutorials out there
If you feel your players could benefit from a little general background on how D&D is done, there are lots of options out there that Googling "How to play D&D" will turn up.
My favorite crash course for learning about D&D is the B movie, Gamers: Dorkness Rising.
Judging fun and frustration
It can be a little tricky judging whether a little exasperation during the game is unhappiness, or just immersion in the tricky situation (especially for a DM, who needs to juggle lots of mental tasks at once). But stopping the action to talk about everyone’s feelings whenever anyone sighs or frowns would wreck any immersion you’ve got going.
Usually any little break in the action is enough to level-set this. When the pizza arrives, the players are leveling up, etc., ask if everyone’s having fun. Let them know that you feel your challenge here is getting the difficulty right for new players. Watch everyone’s reactions. If anyone’s quiet, follow up by asking what they think.
Best Answer
I am afraid you have answered your own question. The first rule of playing RPGs (or anything) is to have fun, so just make sure you also have your share of it.
Now, you are new players, so it is obvious you are going to spend time learning the system, learning how to play with each other, learning how to play at all, learning what type of playing you like most, and learning how to have more fun, and learning... You know the drill.
If you think the game didn't proceed far enough you expected it, you can employ some of these tricks:
To quote numerous smart people who used the same quote I will now paraphrase: