New spectroscopic technologies and techniques are needed to detect and characterize terrestrial planets located in the habitable zones around nearby stars. Existing radial velocity (RV) instruments are limited to 1 m/s single measurement precision at visible wavelengths, and several meters-per-second in the infrared. In order to determine key physical quantities of rocky worlds (mass, density, orbital elements, spin-orbit alignment, etc.), a RV precision one order of magnitude better than the current state-of-the-art is necessary. Such advances would permit the study of planets potentially capable of supporting life.Doppler spectrographs that leverage telescope adaptive optics (AO) capabilities show promise to address many of the systematic effects that prevent current instruments from otherwise achieving more precise measurements. iLocater is a near-infrared (NIR) RV spectrograph being developed for the Large Binocular Telescope (LBT) in Arizona. Unlike seeing-limited designs, iLocater uses AO to inject starlight directly into single-mode fibers (SMF), enabling high spectral resolution while simultaneously mitigating a number of systematic effects. The primary objective of this thesis is to derisk the design of iLocater and facilitate the project's transition from initial development stages to efficient on-sky operations. An end-to-end data reduction pipeline and analysis architecture has been developed to simulate instrument performance (Chapters 2-3). Investigations into detector noise find that persistent charge remaining from previous exposures could introduce unwanted RV uncertainty without careful calibration. Mitigation strategies for persistence and other detector effects are explored (Chapter 4). Earth's Barycentric motion creates multi-pixel lateral Doppler shifts across the detector that cannot be tracked using conventional wavelength calibration; simulations of the spectrograph optical components are used to quantify this effect, along with the impact of spatially varying aberrations, on RV precision when operating near the diffraction-limit (Chapter 5). Simulations of expected on-sky performance were essential in supporting iLocater's successful instrument design reviews at the LBT. It is predicted that the instrument can reach approximately 0.4 m/s single measurement precision on quiescent, bright guide stars provided that telluric absorption is properly calibrated in the YJ-bands. iLocater's first fiber injection system was commissioned in July 2019. The spectrograph and wavelength calibration system are being constructed and assembled at Notre Dame. The thesis concludes with example scientific applications that involve AO and RV measurements, including: high-contrast imaging of stars that exhibit long-term RV trends; and the discovery that two transiting planets that reside in hierarchical triple star systems (Chapter 6).