For example, if I try to remember the name of an actor, I can have hints from my brain telling me "their name starts with an _m_" and "it's a man who played in a movie from the 90's", etc. A memory feels like it cannot be isolated, it always feels like a composition of different elements that, when put together, describe one thing, or many. The more elements (in that case maybe single neurons, or very small group of neurons) are activated the clearer the memory. A Venn diagram of sort where the overlap gets smaller and smaller. This would explain the "this makes me think of…" process, since a certain number of these elements from one memory will overlap with the elements of another one.
This is completely personal and completely unscientific. And maybe this is neuroscience 101… In that case sorry for stating the obvious.
IIRC one of the main cellular mechanisms thought to underlie memory is LTP(Long Term Potentiation) in glutamatergic neurons. There are different kinds of glutamate receptors, but we're interested in the two subtypes of ion channel based(ionotropic) Glut receptors, AMPA and NMDA.
AMPA is sort of your main receptor for propagating signals: it's activated first.
NMDA is much more complicated in that it requires binding both glutamate and another neurotransmitter, glycine, for the ion channel to open. But this ion channel can also be blocked by Mg²+ ions, which for reasons that currently escape me, is removed when the neuron depolarizes. Once NMDA is open, it has the downstream effect of upregulating the AMPA receptor, making more sensitive to future transmission, hence serving as a kind of "memory" of previous signals. I think the open question is more about understanding how memory as we know it emerges out of networks of these neurons, and less about the basic cellular mechanisms. And this is probably only one mechanism of LTP, then you have its opposite, Long Term Depression, which is also involved.
Of course, in science the answer is always more complicated than what can be gleaned from the hand-wavey explanations of some programmer on HN :)
It's relatively easy to induce spike-timing dependent plasticity in vitro, where the background activity is low and the experimenter has almost total control over the pre/post-synaptic neurons' activity. However, in vivo neurons are often bombarded with input from thousands of synaptic partners, breaking the clear correspondence that underlies a lot of LTP/LTD rules. People have gotten them to work, after a fashion, in vivo: Yang Dan's group shifted the orientation of V1 neurons and Dan Shultz's group has some cool backwards conditioning stuff in rat barrel cortex. However, the effects are small and often require a heroic, unphysiological amount of effort, so....there must be more to it than that.
No, we don't.
https://diyhpl.us/~bryan/papers2/neuro/The%20mechanical%20ba...
In all seriousness, though, I'd say that there's a broad dispute in the field between those that believe that memory involves dynamic neural activity involving a multiplexed circuit of neurons that encode many different memories and those (currently led by the Tonegawa lab) that think that memories are associated with individual neurons.