Before tackling the question of a neurone's anatomy, we should ask ourselves just what it is that neurones need to do. Neurones are the basic structural and functional unit of the amazingly complicated system of circuits that is our brain. As such, like a computer's transistors, it must receive information, decide whether or not to fire (integrate that information) and then, if certain conditions have been met, it must be able to fire. It really is helpful to think of them as, fundamentally, biological transistors, because then their structure suddenly seems to make sense.
In this part, we'll tackle the anatomy of a typical neurone. Bearing the above in mind, it should come as no surprise that neurones have an input side. This is basically a tree of fine wires that connect to all the other neurones capable of sending our neurone a message. These wires are called dendrites, and there can be thousands of them. They usually receive information from other neurones, but sensory neurones receive information from the environment (e.g. did a photon just hit this bit of my retina?).
Then there's the cell body, which is boring from out present perspective. It's got the nucleus and all the basic stuff that any cell needs to survive for any decent length of time. (Remember, unlike transistors, neurones do still have to be alive to carry out their function. Their method of working is more complicated than a transistor, and requires continual production of, for example, neurotransmitters, to function.)
Sticking out in the opposite direction to the dendrites is cell's output side - the axon, which the neurone uses to send messages to other neurones. Each neurone usually has one axon, but near its end, the axon often divides into several branches so that it can communicate with numerous nerves. Each communication area is called an axon terminal, or terminal bouton. Basically, it all looks something like this:
So, one neurone's axon would communicate with another neurone's dendrites, and so on, making complicated circuits. If this were the whole story, though, then all neurones would be capable of it acting like wires - passively passing a signal on to the next bit. This is obviously not the case; wires don't make intelligence possible on their own. What is needed is for the neurone to make decisions, however trivial they may seem by our standards. In other words, the neurone must be able to take all the various inputs to its dendrites, and decide whether or not to fire.
More on this later, though. In the following post, we'll go into how nerves integrate their signals and fire, and how the firing is capable of communicating with other neurones.