Let’s say you’re doing a heist game.
Start with the characters on a job. But at first, the GM describes only one character doing something specific (say, actually stealing a painting). The player gets this chance to establish his character’s abilities and style – and to enjoy being in the spotlight.
If you keep the first player’s “spotlight time” short, you can use the other players’ “when-do-I-get-to-play” anxiety for good. They’ll enjoy watching what he does, but they’ll want to jump in – and you’re going to give them that opportunity.
So next the GM presents the lone player with a problem that’s ot of his “class,” or, at least, of a different sort than the kind he’s already shown us he can deal with. (“You get the painting, but the electronic security system locks down the room”) This problem is for another player. Guide the group to understand this: “Security is about to close in. That’s when...” ... and gesture that what happens next is up to whichever player jumps in next.
Now the other players have a unique challenge. For future capers (and for most capers they’ve probably played in the past) the PCs are already “deployed” in the story. In this encounter, the characters are not yet in the story. If this was a movie, the audience wouldn’t have met them yet. So each player has full control of how his character enters the story, where he is, what he’s doing, and what he has been doing. (“The alarms shut back off after the ten seconds it took me to hack the system. Now I’m opening just the doors you’ll need to get out of the building...”). This lets each player design his entrance – in relation to a challenging scenario that you’ve given them. This gives each player a strong sense of what my character does in this group, and in the kind of situations this group is likely to face.
A big purpose for this mechanic is that it can circumvent the first session awkwardness of players trying to guess how their characters can best interact. Now the group is meeting these characters one at a time, just the way we’d meet them if we were watching a movie about them – and just like in a movie, the context makes it immediately clear who this character is and what they add to the group (the hacker, the fixer, the greaseman, the driver, the nick-of-time rogue, etc.). Lots of people are unsure how to start playing a character with a new group. But they’ve all seen movies before, so they all know how characters are supposed to be introduced. As the GM, let your game’s character introductions follow a pattern the players know.