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.
No. A Decker/Technomancer PC or NPC is not required to play SR5. I definitely recommend one though, and if you want to play a Black Trenchcoat game, you have to have a hacker for some runs. No way around it.
I have personally dealt with this issue in my own SR5 campaigns. You have three realistic options that won't inconvenience PCs by forcing them to put Karma into unwanted computer skills.
- Make a Decker/Technomancer GMPC that the players can hire to take along with them on runs. While you make clear in your question that you have considered and rejected this approach, I mention it because ultimately this is the solution I decided to use. Your mileage may vary. I chose to build a cybered-up Technomancer who could fight well in meat-space and used his sprites to hack in the background so he wouldn't slow down or hamper the group with unnecessary Matrix actions. He's expensive to hire, but when the team needs a hacker, he's reliable and he gets the job done.
- Make a Decker/Technomancer GMPC that the players can hire. At first, this may seem identical to the first option. The crucial difference is that if you don't plan on the PCs actually bringing the hacker on the run in question, he doesn't need fully fleshed out stats and personality. Simply decide how big his average dice pool is going to be for the major computer skills and you're done. The important thing for the PCs to keep in mind is that they need to have the hacker do the legwork before they actually start the run. Since the hacker isn't going on the run, he faces far less danger and so you can also charge your PCs less to hire a hacker in this manner than you might have otherwise if you choose. I like to call this the "lazy GMPC" method and when I use it I generally assign the GMPC three values: a small dice pool for actions he is terrible at, a medium dice pool for actions he is passable at, and a large dice pool for actions he specializes in. Computer/Hacking skills will have the large pool, utility skills like Locksmith and Perception will use the medium pool, and then everything else will use the small pool. Small pool might be 3-5 dice, medium pool might be 6-8 dice, and the large pool is usually like 10-12 dice.
- Design your runs so that the PCs don't need a hacker to succeed. You can do this one of two ways: either run a Pink Mohawk style game where the PCs are free to act like action movie stars and simply punch/shoot/blast their way through any obstacles, or have the PCs use social skills such as Intimidate or Con to get people to help them who live or work where the run is to take place. This is similar to hiring a hacker, only more risky since the PCs can never be sure whether they are more intimidating or convincing than the relevant employers or authorities. Philip's answers expand more on this particular solution. In one answer he provides some examples of solid Pink Mohawk play, and in his other answer he gives some examples of run ideas that are light on hacking so your PCs can focus on the action.
Best Answer
Contacts can be many things, for players and GM's. The easiest is to have some basic templates of contacts. Some with very little stats and skills that you use to drop clues/hints or make connections for players.
Other Contact you can flesh out a bit more so you can make a roll to see if they know something or can they repair some specialist piece of equipment, or do they have the street cred to get the item the PC seeks.
Contacts can be used by players to get hold of people or stuff or jobs. It can be used by the GM as plot hooks or twists. And please just because a player has a contact does not mean the contact can or will always help. And maybe sometimes the player have to help the contact too :-)
Contacts can become friends or enemies over time or just stay neutrals.
Your imagination is the only limitation, see how the PC reacts to his contacts, make a note and let that guide how contact feels about the player.