Ok,
First, it is important to know that generally speaking, there are 4 parts to every run, and that not all players are going to be effective at every stage, as that would depend on how they built their characters.
The first part of the run AFTER they take the job, is legwork. They have to (or at least Should!) verify everything the Johnson told them if they don't want surprises. Legwork involves making a bunch of social tests to see if any contacts have any dirt about the subject of the run. Because it is a social test (mostly), this is the time that the Face and others who have invested in contacts and social skills to shine, while those that skipped Social skills and contacts get to sit with their thumbs up their ass because of their own choices. (yes, it sucks, but this is what happens when one ignores social skills and contacts)
The second part after they have done their legwork is the Planning and Gathering step. This is where they make their master plan to get the objective done, and acquire any special gear they need. Again, this is going to be a mix of Social Skills and knowledge skills to get the gear and come up with a plan... Which means again, people who skipped out of Social skills, contacts, and knowledge skills will have less to do.
The Third part is the run itself. Depending on the plan, the objective, and how pear shaped things go, everyone should have had something to do at all stages of this. Hacking doors, providing overwatch, sneaking, introducing lead poisioning to security... this step no one should bored. But because the combination of what they actually do to achieve their goal is limitless, there could be times when a character has nothing to do.... Again this boils down to how the character was built.
Finally there is the Hand Off. this is where the Runners had over the objective and get paid. Some Johnsons however don't like to pay, so they try to screw over the runners... so things can be interesting or boring.... Or the interesting things can happen after the hand over as the players plan their revenge
I notice your experience is all D'n'D based, which is both good and bad. ITs good because at least you understand how the basics of the tabletop RPG work, and have an understanding of the basics of how teamwork in an RPG can come in. It's bad because of the differences between the two systems, and how the way the characters interact with world and what they can do.
In DnD/pathfinder, they have classes. Each class comes with with certain advantages and disadvantages. You know that when you build a Fighter in DnD, you get d10 hp every level, you get the highest BAB, and you can wear and use any armor. You know when you build a mage, you can't use armors, you get d6 hp, you get the worst BAB, and you get spell. In shadowrun, there are no classes per say, Shadowrun uses Archtypes.
Aren't Archtypes and Classes the same thing? No. Archtypes are job descriptions only. They convey nothing to the character beyond a title. (They DO infer a lot however.) Take the Archtype of "Street Sam" (the "Fighter" of DnD). The Archtype inplies that they are a fighting type of archtype, and that is about it. A street Sam can be a cybered up Troll packing heavy armor and heavy weapons. Or they can be an elf who wears very little armor and only uses pistols... There is no set bonuses or disadvantages to being a "Street Sam" that is enjoyed across all Street Sams. When a character in SR get tired of being a Street Sam and choose to "multi-class" into Hacking, they don't just get a host of new abilities and skills: They have to actually buy up those skills and buy their equipment! But, they could call themselves a "Hacker" without investing anything into skills and eqipment if they so choose. (And probably get shot by their own team that was relying on them!)
Which puts the onus back on to the player to make sure this character can do something at every stage of the game. When A player builds a character, they should be asking themselves "What Am I going to do at every phase of gameplay?" and then go from there.
So For example; I want to make a Street Sam for a game. So now I have to think about the phases of the game and what I will be doing and prioritize.
As the Street Sam, Combat will be my focus, so I need to make sure that I can take and deal damage. (lots of options, not going to get into it here)
During the legwork phase of play, to keep with my Combat focus, I am going to get knowledge skills in the areas of Corp Security, Law Enforcement, and Police tactics. (Remember, knowledge skills can be literally anything that is not an active skill! You could have knowledge skills in DC Comicbooks if you so choose!)
However, since legwork also involves talking to actual people, I am going to make sure I have some social skills as well. (They don't need to be huge, but some dice is always better then no dice)
I should also invest in some stealth skills as well. Being good at combat is one thing, but the police have more cops then I can carry Ammo. And when the Shit REALLY hits the fan, The police have access to hardened armor and weapons! (it's called the "Military" and "An on going terrorist Threat" - the Runners!).
Now this is a lot more to think about for the average DnD player, whose usual only major decisions are: Class, Primary Weapon, Primary Armor, Name.
Shadowrun is a lot more fluid style of a game, and it usually takes players (And GMs!) a while to adapt. Take you time, learn the rules at your place and enjoy yourselves!
And as always, If you have questions, come stop by the forums, some of us try our best to help out if we can. But also keep in mind we are a global community that doesn't always agree with each other, so expect some wildly different answers to your questions. Doesn't mean the answers they give are wrong, they just come from a different perspective.