Understanding neuronal firing in the context of Spike Timing Dependent Plasticity When discussing Spike Timing Dependent Plasticity in neurons, when we say that a neuron fires do we mean it fires only one spike? Or do we still say "the neuron has fired" when a train of n spikes was actually fired? 

I find this detail a little confusing when we learn spike timing dependent plasticity (STDP), for example. If the neuron fires only one spike, then the time of firing is precise enough for relative timing between input and output signals to be well defined, and then the theory makes sense. Otherwise, one should give an approximation of the duration of the firing train of spikes and compare it with the duration of depolarization process in the dendrite that triggered this firing. But I can't find any of these anywhere.
Not sure I understand your question correctly.  What is it you can't find anywhere?  I would comment and ask for clarification, but that requires 50 rep which I don't have in this community.  Just tell me if my reply doesn't answer your question and I'll update.

There are two basic ways to describe neurons' firing.  One is rate-based and the other is spiking.
In rate-based neural networks, we look at the intensity, as it were, of a neuron's response to a certain input.
Within the framework of rate-based neural networks, we usually assign numbers to firing rates without attaching any units.
That is, in the model of a neural network, we may say that the response of a neuron has a firing rate of 0.8, but we don't specify 0.8 of what this is (spikes per second, per 10 seconds, per minute...), and it usually doesn't matter either, because all that is important is that it is more or less than the response of another neuron or to a different stimulus.
Note that this presumes that the rate is constant after the stimulus is presented.

In spiking neural networks, we model neurons' responses in much greater detail, designing differential equations which describe the time course of polarization and depolarization, such that a given depolarization can lead to explosive behavior which we call a 'spike'.

Now, many instances of neural information processing can be described very adequately using rate-based abstractions.
This is convenient, because rate-based ANN tend to be much more stable and computationally more efficient.
Also, biological neural firing can be measured much more easily in terms of intensity than in terms of spiking---especially for whole populations.
Therefore, we know more about many of the phenomena we try to model in terms of firing rates than in terms of timing, so rate-based neural networks actually capture our knowledge better.

Only in those cases where we have information about the precise timing of responses, and where we believe it to be important for the phenomena we try to model, does it make sense to accept the much more specific and difficult ontological commitments of spiking neural networks.
Otherwise, we understand what is happening in terms of intensity, not timing, and therefore the actual number of spikes per second do not matter.

The point is, 'firing' refers to related but very different concepts in the two abstractions of biological neurons, and they can't really be compared.
Either you talk about individual spikes in a spiking model, or you talk about rates of spiking over some non-descript unit of time in a rate-based ANN, but trying too hard to compare the two concepts will lead to confusing and nonsensical situations.