How do they isolate a single sound source from a crowd?

It depends on how the audio master panned the sound when he or she was mixing it down as to how successful you might be with most over-the-counter equipment. What kind of recording equipment are you talking about?

You can do it with a pinpoint mic. There are two basic types: the boom mic that looks like a long yagi antenna or a dish. They work on different principles but accomplish the same task. The longer the boom mic the more selective. The larger the dish, the more selective. If you have the access the best is still an RF mic on the subject.

@worriedguy Good point, I read the question as isolation from pre-recorded material.

It is from pre-recorded, it would be for any recording, but I would like a boom mic.

If you’re asking how to remove an isolated voice from a crowd using a single recorded audio track (or microphone signal) of mixed voices all talking at once, I don’t think that’s possible.

Our brains do it routinely, of course, which is how cocktail parties are possible. In theory what the brain can do, a computer could do. As a signal-processing problem, however, using present-day engineering technology, we don’t even know how. Give it at least a century…

If the voice is pitched differently from the others (such as a lead singer with back-up singers) it might be possible, using narrow bandpass filters, to pick out just the lead voice based on its fundamental pitch. It wouldn’t sound right, however, because its mix of overtones that give rise to the voice’s timbre & character would be lost in a smear of higher frequencies.