If due to some reasons a small portion of our neurons die, how does our body remake them?
Evolution set us humans up to not regenerate our neurons on the whole, which is a pity since we can regenerate our liver cells, so it's not an impossible feat. If neurons die because you drank too much, banged your head, or just because they got old, they are gone. If this death is accelerated like in Alzheimer's disease, you can literally see holes in the brain autopsy. That said, we now know that in a few exceptional areas of the brain, neurons do regenerate. It's not many cells but it's something. The two areas known to date are the dentate gyrus of the hippocampus (DG below) and the subventricular zone of the lateral ventricles (LV). See the green zones in the image below.

From Ernst &amp; Frisen PLoS Biology 2015 (CC-by)
In those areas, like elsewhere in the body, new cells are made from stem cells, that is infant-like cells that have the potential to become many cell types. If we could only understand why some cells regenerate and others do not, we might be able to promote this. Alas, our current understanding is woefully incomplete. We'll need more research # # # before we can dream of regenerating our neurons.