Measuring the Sebecke coefficient is rather tricky, especially measuring the actual temperature at the contact points. Much of the difficulty is likely in preparing the samples. It can be relatively easy with large samples of low thermal conductivity material, but rather tricky with brittle, high conductivity materials.
The general idea would be measuring thermal EMF and temperature difference. In the simple form this could be with 3 material junctions on both sides. To form 2 thermocouples: one could be something like copper and sample and the other could be the same copper and constantan.
The setup really depends on the samples - likely no one version fits all solution.