How are the thickness of ice sheets from previous glaciation periods determined?
There is no direct way to determine past ice thickness. The only solid information that exists are past areal extent. But, even this information is not necessarily clear since later advances may have overridden the past terminal positions and dating may not be exact. A main issue is the synchronicity of all such positions. 

With a past extent it is possible to calibrate numerical ice sheet models, based on our understanding of ice physics and dynamics and generate likely ice sheet configurations. Such models generate a three-dimensional ice sheet which includes ice thickness. In essence this is the best possible scenario for estimating such past ice thicknesses. Advanced models also include some form of isostacy depending on the overlying ice load. For the last Glacial Maximum, the rebound values are also used to constrain the ice sheet geometry. 

The problem is, however, that the response of the Earth's crust to loading depends on the loading history and it would be possible to accomplish similar results with different scenarios since the depression of the crust is in part the loading but also the time scale of the loading. For a long time we though the latest glaciation was one long period of glaciation but we now know that, at least the Fennoscandian ice sheet, experienced two major advances, the mid-Weichselian and the Last Glacial maximum and both were relatively short in duration. This allows us to modify the loading history of the latest glacation. With the earlier glaciations, we do not yet have such detailed loading histories and are thus not able to make detailed models of ice thickness.

It should be added the the understanding of the variations of the last ice sheet come from a series of indirect sources such as sea-level changes, paleo-climate records e.g., (ice cores) and interstadial paleoclimate reconstructions. This means that as our understanding of these indirect records are improved, we can also improve our ice sheet forcing. Add to that uncertainties about basal conditions beneath past ice sheets that affect their dynamics and it is easy to see that past ice thickness values are uncertain. We can, however, obtain reasonable estimates from the models which could be accurate to within, perhaps 500 m (my guestimate).