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How do runners typically get their jobs? Direct phone call?
It depends. Usually it'll be as was stated earlier; an in-person meetup that's offered by one's fixer. Depending on one's specialty, though, you might get contacted by someone you already know. Lets not forget that contacts often have their own agendas, and if you owe them a favor you'll get called for a job. Or maybe, say for a hacker, you'll get a job over the Matrix or just stumble into something.
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How much time do they typically get to prepare? Are most runs like "Can you pull it off tonight?" kind of deals?
"Do it tonight" gigs are usually rare. If you're hiring elite disposable assets, you're doing it to get a very specific job done. Those jobs often require specific tools, and unless you tell the guy up front what he's doing, before even meeting him, he's not going to have them. More often than not, he'll need to acquire something unique - an ID card to get into a building, for example. These things take time, and moreover saying "I need you to bring a gun and plenty of ammo to hose down a group" is gonna get you busted by the cops.
More frequently, if a job needs to be done quickly, it will either be relatively simple with any and all necessary items proved (here a gun, go here, kill that guy with such and such problems you'll encounter), or will be handled in-house (I.E. the company's own private forces will take care of it, such as retrieving a document that some runners stole.)
For jobs with longer time-frames, it'll be expected that the runners get their own intel and do their own research. That'd be called "legwork."
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How do the runners prepare? (This is the part I'm most interested in hearing about)
Legwork is usually a vague part of storytelling, and is more like a game of 20-questions than anything. "What kind of security do they have" is a pretty formal question to ask the Johnson, but actually getting the information is pretty tricky. If you're hitting a corporate structure, you can probably hack in to get a schedule of when various people are on duty, and who has what access. Mages can astrally scout places out, but if there's an opposing mage that'll tip the enemy off. You can hit up your contacts and see what they know - that's usually helpful.
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What do you find that runners typically buy before a run? Anything?
Usually, they've stockpiled ammo. Sometimes the procurement of fake IDs is necessary. Sometimes a small safehouse is nice. Characters will often have emergency bags - a first aid kit, a gun, some ammo, a fake ID, some cash, maybe a flashlight and some other survival gear like a knife and clean clothes - stashed through the city in various places. If they need something specific, they'll get hold of it.
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How do they find out about what is in store for them in the compound?
Legwork, legwork, kegwork and legwork.
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How much info about the compound and its security can they typically get before the run?
It depends. As I said earlier, skilled hackers can get personnel files. Mages can do recon. A physical casing of the joint can yield a knowledge of where the exits are and what physical barriers are in the way. No matter what, though, unless something actively disrupts the system, its pretty static - Bob shows up to work on time, while James is pretty bad at that. So if you know James isn't so useful, maybe you can buy him off...
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Spell out for me everyone's role in the caper: Samurai, Decker, Mage, Rigger, etc.
Streetsam: These guys are usually quick on inits, and quick on the trigger. They mow down low-grade security, but keep 'em away from Mages. Someone used the MMO/D&D ideal to compare them to fighters? That's pretty accurate.
Decker/Hacker: Get intel, open locked doors, and hopefully know how to handle a gun to stay alive.
Rigger: Meh, I've never been a fan of drone-swarms. But yeah, these guys will drive your vehicles, often playing taxi, and often keeping you alive in any kind of chase. I've once seen what happens when Riggers get hold of helicopters.

PhysAd: Adepts are usually your melee guys; they can get in close and chop dudes up. But sometimes they'll be gunners, just as sometimes Street Sams'll be swordsmen. It all depends. They usually fare better against magic, and less well against bullets.
Mages: Anti-Street-Sam, but otherwise they're jack-of-all-trades. Its rare to see a mage without at least one combat spell, while others are decked out with 'em.
Faces: They socialize, but they also often double as stealth guys who can infiltrate. Think James Bond.
Overall: Each team is unique. Each mission has its own things. Don't necessarily re-write charsheets or spend massive amounts of GK to deal with any one mission, but do be prepared to procure individual, specific goodies to get by a problem.
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How do they make their get-away? In a car that was hidden?
Typically, yes. Ideally you want to get in and out unnoticed. Ideally, this involves some kind of distraction or effort to avoid detection. If you
are busted, however, you can either shoot your way out or drive as fast as you can. In theory, this is pretty hard - there's lots of ways to track crooks today, let alone in 2060.
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How do they get paid?
Half up front, half up later; or some variant thereof. The upfront is a show of good faith as well as a down payment on any goods that are needed to get the job done, the after is the real payday. And that's not a bad system. Oftentimes the bigger question is the actual
how they get paid. Do they have a group account that the Johnson can deposit nuyen in? Or do they get certified credsticks? Does the Johnson pay the group as a whole, or does he pay each one individually?
It can be very interesting to watch the Mage want to buy the formulas for Spell XYZ, while the Rigger wants to buy a new vehicle, and both need a little extra cash from the Adept who has all the gear he needs and wants to keep his half-up-front.
Hope this helps!