showed patience and understanding. He gave me the opportunity to work on a variety of interesting projects, from graphene, to superconducting amplifiers, to the results discussed here. Most of all, Keith taught me to be more decisive, to take more risks, and to do whatever it takes. Our theory collaborators on the squeezing project, Aashish Clerk, Florian Marquardt, and especially Andreas Kronwald, gave essential support before, during, and after measurement-taking.Although they sometimes seemed puzzled at the number of ways that things can go wrong in experimental work, they showed great patience as we tried to make their proposal a reality.I couldn't have made it through grad school without the support of my friends: Paul, Branimir, Helge, Alice, Tristan, Chris, Kris, Doron, Mo, and Carly. They gave me something to look forward to throughout the week, and something to talk about other than grad school. where an optical or microwave cavity is coupled to the mechanics in order to control and read out the mechanical state. In the proposal, two pump tones are applied to the cavity, each detuned from the cavity resonance by the mechanical frequency. The pump tones establish and couple the mechanics to a squeezed reservoir, producing arbitrarily-large, steady-state squeezing of the mechanical motion.In this dissertation, I describe two experiments related to the implementation of this proposal in an electromechanical system. I also expand on the theory presented in [30] to include the effects of squeezing in the presence of classical microwave noise, and without assumptions of perfect alignment of the pump frequencies.In the first experiment, we produce a squeezed thermal state using the method of Kronwald et. al..We perform back-action evading measurements of the mechanical squeezed state in order to probe the noise in both quadratures of the mechanics. Using this method, we detect single-quadrature fluctuations at the level of 1.09 ± 0.06 times the quantum zero-point motion.In the second experiment, we measure the spectral noise of the microwave cavity in the presence of the squeezing tones and fit a full model to the spectrum in order to deduce a quadrature variance of 0.80 ± 0.03 times the zero-point level. These measurements provide the first evidence of quantum squeezing of motion in a mechanical resonator.