So, as has been mentioned elsewhere, neurons pick up the pulses or spikes of activity that travel away down the axons of its neighbouring neurons. This activity jumps the gap at the synapse on to the dendrites of the receiving neuron. The activity the neuron picks up can either be excitatory (making it more likely to generate its own spike) or inhibitory, but if there is enough excitatory activity the neuron responds by generating a spike of its own that travels away down its own axon.
The spikes are like Mexican waves of chemicals moving in and out across the walls of the axon which is hollow. The atoms that move in the wave all carry an electrical charge, so the propagating wave is, in some ways, like an electrical current in a wire. However this analogy can be pushed too far. The brain is not an electrical device in the usual sense (which would involve electrons moving through a solid or a gas) the brain is a liquid phase machine and the spikes are movements of charged atoms - or ions as they are known.
The only way to detect an individual spike in an individual neuron, is stick a glass needle into the brain and get it as close to the neuron as possible. This is fraught with difficulty and interpretation of the results can be very tricky.
However, groups of neurons tend to fire more or less at the same time, and the axons of the group are, more or less, all pointing in the same direction in many cases. The total resulting current is large enough to be detected by placing coils on the scalp. This technique is known as EEG (electroencephalography). The EEG is incredibly useful because it records exactly when the activity happens but, frustratingly, it is very difficult to pin down exactly where the signal came from - only a very rough answer is usually possible. And in any case this technique is limited to activity that is near the skull (mostly the outside 4mm or so of the brain known as the cortex).
If something causes the brain to generate more spiking activity than usual, then, between 2 and 6 seconds later, there is a corresponding increase in blood flow in the area of activity. Although this increase in blood flow is generated way after the event, doesn't directly measure the activity of the neuron, and contains no fine timing detail, it does have the the huge advantage of being easy to locate using a technique known as MRI (magnetic resonance imaging).
From: Martin’s Vastly Oversimplified and Woefully Incomplete Guide to Everything in the Brain as featured on the Brainsex website.