how do presynaptic and postsynaptic neurons work?

The presynaptic neuron terminal is the one that releases a neurotransmitter in response to an action potential.

The postsynaptic neuron is the one that receives the neurotransmitter and may undergo an action potential (and become a presynaptic to the next nerve cell) if the NTs stimulate the cell enough.

Presynaptic Neuron

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Easy, by measuring from the postsynaptic neuron, you can see how many neurotransmitters were actually received. Knowing the rate of neurotransmitter response, release can be determined. Besides, its more practical to do it this way. The derivative of the change in rise time is the slope. In other words, the slope describes the rate at which the change in rise time occurs. Finally, there are several factors which could contribute to both the change in rise time and the rate of change. Namely, change in pH and introdution of various bacteria.

Pretty complicated question- It's difficult to determine what you mean by "work."

One possible short answer would be:

Presynaptic will be set off (or "work") by the action potential.

Postsynaptic receive membrane potentials, and "work" through spatial and temporal summation.