Okay, here is what actually happens. Neurons don't usually differentiate. So instead, cancerous neuronal cells are commonly used (neuroblastoma cells). Basically, these neuronal cells have decided to divide rapidly. You simply place these cells in a serum of growth medium consisting of protein, sugars, and salts and watch them divide over the course of a few days.
It would be nice to use stem cells instead or cancerous cells... but that is another thread entirely.