I am trying to understand how the length and diameter of a compartment are specified. For example, in the Hodgkin–Huxley model, we only have conductances specified in $\rm mS/cm^2$. How do you specify that a compartment is say $100 \mu\rm m$ long?
In a single-compartment model, you do not have spatial dimensions. Sometimes this is not a problem, for example in the stomatogastric ganglion of C. borealis, in which the neurons have a mechanism to scale the signal with distance by modifying the "effective reversal potential" (Otopalik et al., 2017). In the case of one of these models, it would be sensible to either make an approximation of the cell surface area (Liu et al., 1998 for example) or to use parameters which are normalized by the surface area, to whose explicit numerical value we remain agnostic. One would do this by using a membrane capacitance in microfarads per centimeter squared for instance (typically about unity) and then use maximal conductances in millisiemens per centimeter squared.
This way, the natural units for current divided by capacitance are mV * mS/cm^2 * cm^2/uF, or equivalent to mV/ms.
If you wanted to model multiple neurons with a decay factor, you could either use the cable equation and explicitly input the current into the descending neuron following that, or make a neuron with multiple compartments.