This post is a decent first approximation. But it is important to remember that even successful communication is almost always occurring on more than just one of these levels at once.

Personally I find it useful to think of communication as having spontaneous layers of information which may include things like asserting social context, acquiring knowledge, reinforcing beliefs, practicing skills, indicating and detecting levels of sexual interest, and even play. And by spontaneous layers, I mean that we each contribute to the scope of a conversation, and then those contributions become discerned as patterns (whether intended or not).

Then iterate this process a few times, with my attempting to perceive and affect your patterns and you attempting to perceive and affect mine. Add some habitual or built-in (it's extremely hard to tell the difference) models in the mind to start from and it seems simple (to me) how something as complex and variable as human communication can arise.