Saying we have no idea at the synapse level seems a little too strong. The abstraction level above is hard, but at the level of a synapse it goes something like this: In an upstream neuron, through some internal cell signaling that usually ends in Ca2+ increasing, vesicular fusion happens and releases neurotransmitter in the synaptic cleft. The neurotransmitters bump into the cell membrane of the downstream neuron, where there are receptors. By binding to the receptor, further cell signaling happens in the downstream neuron.
I'm skipping over a whole lot other important mechanisms, and the above is very simplified, but my understanding is that we know the mechanics of how two neurons connect with each other. Much more difficult is understanding what happens the next abstraction layer up, when you try to describe the brain as meaningful small group of neurons instead of individual synaptic connections.
https://en.wikipedia.org/wiki/Neural_circuit shows a few interesting patterns, but we're clearly not at a stage where we can describe the brain in terms of elementary circuits building blocks. However, the brain is also not a giant completely disorganized mass of neurons. As we increase our ability to map out connections (as far as I can tell, a pretty destructive and delicate process), we should be able to map out more common patterns. Which is generally a good starting point in trying to reverse engineering a little bit of sense and meaning out of large opaque blobs of concentrated confusion
(Full disclosure: not a neuroscientist. The above may also be terribly wrong)
