The marriage between Rydberg physics and ultracold atomic systems have hatched so many fascinating achievements. The exaggerated properties of Rydberg states, combined with the pristine environments provided by the ultracold atoms, can lead to realizations of exotic physical systems. One particularly innovative direction that emerged recently is to use microwave-frequency transitions between Rydberg levels to simulate the dynamics of a particle hopping between lattice sites. Such approach, referred to as Rydberg synthetic dimensions, falls under the broad scheme of quantum simulations. Here we present description of the infrastructure used for Rydberg excitation and coherent microwave transitions, which are essential to the realization of Rydberg synthetic dimensions. We will also present experimental results on simulating the Su-Schireffer-Heeger Hamiltonian, a canonical model with paradigmatic importance in topological physics.