A single neuron has something on the order of thousands of connections; trillions of these synapses in all, billions of neurons. Neurons are effectively state machines; stuff adds up until a threshold is met, then it fires. The neurons are pretty much continually firing with the rate of firing being important; but with the rate of firing being only part of what they are doing. There's also the chemical portion, involving several chemicals whose job is to temporarily increase or decrease sensitivity of synapses and such. And then there's the slow change in connection strength of synapses.
Information/memories are stored in just about every part of the system; which is why memories have vastly different properties. Very short term memories are effectively feedback loops; a web of interconnected neurons repeating a pattern of activity or similar. Long term memories are a bit more interesting; they are mostly stored in the patterns of the brain's connections and their strengths. As such, there is no particular place you can point at and say 'memory X is stored there,' as 'memory X' consists of a variety of pieces scattered throughout a variety of regions of your brain, all or most of which overlap with 'memory Y' or 'memory Z,' such that you can only say 'that neuron right there is kinda sorta related to memories X, Y, Z, A, G, and P.'
Neuron relationship status: It's complicated.