The radial velocity (RV) technique is used to identify signatures of exoplanets orbiting their host stars. Doppler measurements constrain the minimum planetary mass and are used to determine orbital parameters of the star-planet system. In order to probe terrestrial planets, an RV sensitivity of 10cm/s is required, an order of magnitude improvement on existing instrument capabilities. This research investigates the RV precision of an adaptive optics (AO) fed single-mode fiber (SMF) RV spectrograph. RV measurements with an SMF spectrograph are unique as the spectral resolution is limited only by diffraction, as opposed to atmospheric seeing.  We demonstrate for the first time, the injection of starlight into SMFs using adaptive optics (AO) at the Large Binocular Telescope. We measure an absolute injection efficiency of 20%. High speed AO corrected images of the stellar point spread function are characterized to quantify optical aberrations. We determine low order residual wavefront errors are the limiting factor on injection efficiency. The photon-noise limited RV precision is calculated by modeling an RV spectrograph combined with fiber coupling efficiency measurements and simulated spectra. Measurement uncertainty resulting from instrument effects is quantified by systematically studying the individual perturbations of numerous optical, mechanical, and thermal effects. It is found that a sub-m/s total RV uncertainty is possible on mid M-type stars with a diffraction-limited optical system.  Finally, the use of single-mode fibers has unique optical consequences for the RV instrument not experienced by existing multi-modal instruments. While the fraction of light bound to the fiber waveguide propagates as a single mode, each spatial mode is comprised of two polarization modes. Bimodal polarization effects were measured at the LBT and assessed in the context of RV spectroscopy. Results suggest that high resolution Doppler spectroscopy at the diffraction-limit is capable of detecting terrestrial mass exoplanets orbiting bright M-type stars.