In this dissertation, we present work on a quantum hybrid device comprising of a trapped calcium atom and a superconducting LC resonator. This hybrid device is a first step towards building a hybrid quantum computer that can take advantage of the different properties of atomic and superconducting quantum systems and combine the best characteristics of both. We model a trapped ion as an LC circuit and calculate its coupling to a mode of an LC resonator. Further, we optimize the trap geometry and placement of coupling electrodes to increase the coupling. We also outline the manufacturing process and simulation of the trapping potentials for the surface traps used in this work. Finally, we report on initial experiments coupling a trapped ion to a resonant mode of the LC resonator, increasing the heating rate to 220 phonons/ms on resonance versus 0.5 phonons/ms without additional heating from the resonator. The ratio of the heating rates for the two secular frequencies of the ion confrm our simulated coupling rates.