Where did this estimate come from?
Neuroscientists Bradley Voytek of UCSF and Paul King of the Redwood Center for Theoretical Neuroscience at UC Berkeley weigh in on Quora.
How do we know that there are 100 billion neurons in the human brain?
The easiest way to estimate the number of neurons in the brain is to count how many are in one part of the brain and then extrapolate out for the rest of the brain’s volume. But this method has a few issues.
1. The brain’s neuronal density isn’t uniform. For example, the cerebellum (the purple-colored structure in the bottom back in the image below) contains about half of all the neurons in the central nervous system, but it is well below half the volume.
2. It’s hard to get an estimate even for one brain region, because the neurons areso dense and intertwined (and mostly clear!) that they’re hard to count separably. One method is to use a staining technique to make neurons visible enough to count them. A classic method is the “Golgi stain” (named after Nobel prize winner Camillo Golgi). This method stains only a few percent of neurons (no one’s quite sure why). So in the stain below, even though only one neuron is visible, there may be hundreds more in that space that you can’t see because they didn’t stain.
Using this method, you estimate what proportion of neurons get stained, count the number in some patch of brain, then extrapolate. But you’re introducing two variables for your guess here! Not very accurate.
The new method  that gives us the 86 billion figure is… interesting.
The method involves dissolving the cell membranes of cells within the brain and creating a homogeneous mixture of the whole lot. You then take a sample of the soup, count the number of cell nuclei belonging to neurons (as opposed to other cells in the brain such as glia) and then scale up to get the overall number. The great advantage of this method is that unlike counting the number of neurons in one part of the brain and then extrapolating from that, it gets over the problem that different brain regions may have more or less densely packed neurons.
So there you go. This is the latest plausible estimate. But you notice that to do this, the researchers are still using the extrapolation method.
Maybe new crowd-sourced efforts such as the Human Connectome Project eyewire game  will eventually provide us with a more accurate number that doesn’t rely so heavily on estimation.
 Equal numbers of neuronal and nonneuronal cell… [J Comp Neurol. 2009]
(Edit: Ha! Looks like Paul King and I gave almost the exact same answer at almost the exact same time.)
Now for Paul King’s Answer
Neuron density for different types of neural tissues can be estimated by taking a slice of tissue, putting it under a microscope, and counting individual cells that have been stained for visibility on a marked grid (similar to how white blood cell counts are done). However this type of estimation is specific to the neural tissue being evaluated.
For example, the cerebral cortex is a sheet of neurons with a surface area of 2500 square cm (equivalent to 50×50 cm or 20×20 inches), and 2 – 4 mm thick. So an estimate of neuron density can be made for cortical tissue based on slices, which people put at around 50,000 cells per cubic mm.  Multiplied out gives 25 billion neurons for the cerebral cortex.
This image shows the cerebral cortex how it is usually seen (left), and what it looks likes if “inflated” to form a flat sheet of neurons (right):
The white matter of the brain, just below the 2 mm surface, is almost entirely axons, not neurons.
The cerebellum has very tiny neurons in it, so even though the cerebellum is less than 10% of the brain by volume, some say it has more neurons in it than the rest of the brain combined (50 billion by one estimate).
If one assumes that the cerebellum and the cerebral cortex together account for at least 2/3 of the neurons in the brain, one can then get to an estimate for the whole brain.
But clearly there is a lot of “guestimating” going on.
The mass counting method that Bradley Voytek mentions is an interesting new direction, however it produces a number for the glial (non-neuron) cells that is 10x smaller than the manual method, so it is still controversial whether this method can be trusted.
—- Harvard ultrascale imaging website analyzing a cubic mm of cerebral cortex. (http://crl.med.harvard.e