Calculating effective SSN (sunspot number)
The effective sunspot number $R_{\text{eff}}$ is calculated through a mix of observations and model calculations. It focuses primarily on some parameter called the frequency of the ionosphere F2 layer, denoted $\text{foF2}$, the highest frequency of electromagnetic radiation which can be reflected off the F2 layer; it can be observed as well as computed based on a certain model (real-time observational data from stations around the world is available here). More information on $\text{foF2}$ can be found on this page.

The mean-squared error between the observational value $\text{foF2}_{\text{obs}}$ and the calculated value $\text{foF2}_{\text{calc}}$ over observations by $n$ stations is
$$\Delta=\frac{1}{n}\sum_{i=1}^n\left(\text{foF2}_{\text{obs},i}-\text{foF2}_{\text{calc},i}\right)^2$$
where $_i$ denotes the value at station $i$. $R_\text{eff}$ is defined to be that chosen sunspot number such that $\Delta$ is minimized.

This is just an application of a least squares method to fit a model framework to match observations. An example of this using the Simplified Ionospheric Regional Model (SIRM) is Zolesi et al. (2004), although the procedure for calculating $R_\text{eff}$ was first proposed by Houminer et al. (1993). This was introduced to augment or replace something called the 12-month smoothed sunspot number, $R_{12}$, which is entirely based on observations. Zolesi et al. write


  It is therefore expected that during periods of relative ionospheric quietness, when the observed $\text{foF2}$ value is much closer to the model predicted median values, the $R_{\text{eff}}$ does not differ much from the $R_{12}$. On the contrary, during periods of ionospheric activity, the $R_{\text{eff}}$ should have large difference form [sic] $R_{12}$.