How to interpret neuron spiking models one comes across in literature? Background

I'm in high school currently conducting research (obviously it is relatively rudimentary compared to what is being done in the labs, etc.) in computational neuroscience. 

I'm dealing with multiple datasets each containing time series data for a majority of neurons in C. Elegans (the dataset is the one used in Saul Kato's Global Brain Dynamics Embed the Motor Command Sequence of Caenorhabditis elegans). 

I'm looking to do a pairwise comparison of each neuron in every dataset; if $N_{ij}$ is the $j^{th}$ neuron in the $i^{th}$ dataset, then I will do a pairwise comparison of all neurons in the $j^{th}$ column. 

Question

I'm going through this paper which proposes a method of comparing time series data across neurons. The paper uses this spiking model: 



I'm wondering how neuroscientists approach such models they read about in literature; how they dissect it mathematically, what crosses their mind when they look at these models, etc. and where I can go to gain a rigorous foundation to truly and intuitively understand the models I read about in the future.
Read dayan and abbot "theoretical neuroscience" 
Learn differential equations 
Know the relationship between voltage, current, resistance and conductance
Differential equations is absolutely essential though. you don't need to learn to solve them (the computer will do that for you), you just need to learn to know what they mean.    
How do researchers translate observations of nature into symbolic, mathematical approximations/models of these phenomena? By gaining intuition of how the model components relate to empirical observations. it is relatively rare that someone comes up with a new model from scratch. most of the time people retool or remix previous models.