Additional contributions from processes such as diffusion or adsorption add extra circuit elements, giving further semicircles and lines on the plot. Powerful numerical analysis programs are available to deconvolute the measured response to its components. Even so, the analysis of impedance data can be something of a black art and the literature abounds with arcane equivalent circuits and explanations. For more detailed notes have a look at Gamry 's site. In those happy days I generated low frequency sine waves with a slowly rotating pulley and a length of resistance wire and analysed them using a scope or an X-Y recorder and Lissajous figures.
Current equipment does it all at the push of a button.