A neuron is a device for processing information. It receives a bunch of signals through dendrites, and if it decides there are enough of them, it passes them on through the axon. Nothing complicated. But if you connect them into a really large crowd, they can send that signal in the right direction and transform it in a way that strongly resembles intelligence.
We'll start drawing with an oval nucleus.
Around it, we'll draw a body with a crown of dendrites that look like pointed branches.
We'll add a long axon tail covered with ovals of the myelin sheath. It ends in a tree of projections that resemble branches with flat tips.
The result is a quite recognizable neuron.