Axons and dendrites (the output and input projections of neurons) are not like wires. They are fluid filled tubes with porous walls. The spikes that travel down the axons, and are recreated in the receiving dendrites, are like Mexican waves of chemicals moving in and out across the walls. The atoms that move in and out all carry an electrical charge.
So the propagating wave is not really like an electrical current in a wire, and the brain is not an electrical device in the usual sense, which would involve electrons moving along in the direction of the current through a solid or a gas. The brain is a liquid phase chemical machine, and the spikes travel at right angles to the movement of charged atoms (or ions as they are known).
Think of the Mexican wave again, the wave travels left to right, but the people just stand up and sit down.
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, severely limiting, and interpretation of the results can be very tricky.
However, large 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 effective current is large enough to be detected by placing coils on the scalp. This is not like picking up a radio signal because the field that is detected changes relatively slowly and is not broadcast. This 'coils touching the scalp' technique is known as EEG (electroencephalography). The EEG signal is incredibly useful because it records exactly when the activity happens and the 'shape' of the activity in time. 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).
An alternative way to measure brain activity relies on the idea that increased activity results in increased blood flow. 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 same area. Although this increase in blood flow is generated long 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 (even deep below the cortex) using a technique known as MRI (magnetic resonance imaging).
Because of the accuracy in location that is possible, MRI is the way most of the 'images of brain activity' you see in scientific reports are generated.