Literary Latin is a special case of Latin. For the most part, it is the only Latin that we have, but we can construct some information about how people on the street. This Latin would be called colloquial Latin or Vulgar Latin. While it is often associated with class differences and with educational level, one should not forget that even you ever-so-educated professor talks differently when she is at a football game from the way she talks when she delivers a paper at a professional organization. In English, in colloquial situations we take more liberties and have more language resources. It is for this reason that one of the most common resources for the renewal of the literary language is colloquial speech. That is an interesting irony, since the literary language almost always presents itself as better, more precise, more refined and so on.
Indirect Discourse is an exellent example of how Literary Latin relied on more limited resources than Colloquial Latin. If you think of how to report the words of another in French (il dit qu'il ….) you will notice what looks like the remains of a Latin relative: qu'. That is exactly what qu' is; it is the Latin quod. And that tells us, not only that some Romans reported speech by saying dixit quod …, but that this form of noun-clause was the normal expression in Colloquial Latin. In other words, it was so popular that dixit quod … survived and became dit qu' in French, while the Classical Latin, dixit + accusative - infinitive passed quietly away.
Here's another example of how we know some things about Colloquial Latin and how it was different from Literary Latin. In all Romance Languages the word for "horse" is derived from a word, relatively rare in Classical Latin, caballus, -i, M. This word gives us "cavalier" and "cavalry." And the fact is that the Classical Latin word for horse, equus, -i M., only appears in Literary or Technical English: "the equine features of his equestrian rank." This tells us that your everyday Roman called a horse a caballus, not an equus.