The party usually operates as one unit. When they come to a major decision point, they get everyone's perspective and maybe take a vote. When they come to a complicated situation, each person contributes what they can to the course of action. And unlike in film or TV, the "camera" is pretty much always pointed at the party the entire time, with no occasional dramatic cuts to the villain's lair to show him talking to his cronies or whatever. That's the idea, anyway.
This does not always work out. Sometimes just because of circumstances outside of anyone's control, but oftentimes it's because of a deliberate decision. The party will eventually find themselves in a situation where they ask, "should we send the rogue to scout up ahead alone?" Even most experienced players will be uncomfortable taking the risk, and still always try to return to the status quo as soon as possible. "Don't split the party" is one of the most oft-repeated mantras in tabletop gaming.
But I have done it a fuck ton and it's been fine.