Among the research topics needing to be addressed to further the development of phased array feeds (PAFs) for radio astronomical use are challenges associated with calibration, beamforming, and imaging for single dish observations. This dissertation addresses these concerns by providing analysis and solutions that provide a clearer understanding of the effort required to implement PAFs for complex scientific research. It is shown that calibration data are relatively stable over a period of five days and may still be adequate after 70 days. A calibration update system is presented with the potential to refresh old calibrators. Direction-dependent variations have a much greater affect on calibration stability than temporal variations. There is an inherent trade-off in beamformer design between achieving high sensitivity and maintaining beam pattern stability. A hybrid beamformer design is introduced which uses a numerical optimizer to balance the trade-off between these two conflicting goals to provide the greatest sensitivity for a desired amount of pattern control. Relative beam variations that occur when electronically steering beams in the field of view must be reduced in order for a PAF to be useful for source detection and imaging. A dual constraint beamformer is presented that has the ability to simultaneously achieve a uniform main beam gain and specified noise response across all beams. This alone does not reduce the beam variations but it eliminates one aspect of the problem. Incorporating spillover noise control through the use of rim calibrators is shown to reduce the variations between beams. Combining the dual constraint and rim constraint beamformers offers a beamforming option that provides both of these benefits.