How do speech recognition algorithms initially separate a continuous sound wave into discrete chunks?

I'm a beginner in the middle of Andrew Ng's Machine Learning class, and its got me thinking about some machine learning applications. Particularly, it's application in speech recognition. I figure that once you have the sound wave in discrete chunks, it becomes like a classification problem we discussed in class.

However, that's not the case, at least not initially. I'm wondering what types of algorithms are out there for handling continuous streams of data, as this doesn't seem to be covered in the class.